The Eighth Congress of Romanian Mathematicians

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List of talks

I. Algebra and Number Theory

Special session: Local rings and homological algebra. Special session dedicated to Prof. Nicolae Radu

II. Algebraic, Complex and Differential Geometry and Topology

Special session: Geometry and Topology of Differentiable Manifolds and Algebraic Varieties

III. Real and Complex Analysis, Potential Theory

IV. Ordinary and Partial Differential Equations, Variational Methods, Optimal Control

Special session: Optimization and Games Theory

V. Functional Analysis, Operator Theory and Operator Algebras, Mathematical Physics

Special session: Spectral Theory and Applications in Mathematical Physics

Special session: Dynamical Systems and Ergodic Theory

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

Special session: Mathematical Modeling of Some Medical and Biological Processes

Special session: Mathematical Models in Astronomy

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

Special session: Logic in Computer Science

IX. History and Philosophy of Mathematics

Ordinary and Partial Differential Equations, Variational Methods, Optimal Control 

(this list is in updating process)

Yildiz Technical University, Turkey
Title: Some inequalities about the eigenvalues of a two terms differential operator and the sum of the eigenvalues of that operator (details)
In this work, we find an asymptotic formula for the sum of the eigenvalues of a differential operator L in the space $L_{2}(0\pi;H)$ . Here, H is a separable Hilbert space.
BEREANU Cristian
University of Bucharest and IMAR, Romania
Title: Prescribed mean curvature of manifolds in Minkowski space (details)
\documentclass[12pt]{article} \usepackage{latexsym} \usepackage{amssymb,amsmath} \usepackage{amsfonts} \begin{document} CRISTIAN BEREANU\\ Title: Prescribed mean curvature of manifolds in Minkowski space \\ Abstract: In this talk we present existence and multiplicity of classical positive solutions for Dirichlet problems with the mean curvature operator in Minkowski space. We use a combination of degree arguments, critical point theory for lower semicontinuous functionals and the upper and lower solutions method. \end{document}
BOCEA Marian
Loyola University Chicago, U.S.A.
Title: Relaxation and Duality for the $L^{\infty}$ Optimal Mass Transport Problem (details)
The original mass transport problem, formulated by Gaspard Monge in 1781, asks to find the optimal volume preserving map between two given sets of equal volume, where optimality is measured against a cost functional given by the integral of a cost density. After reviewing some aspects of this classical problem, I will describe recent joint work with Nick Barron and Robert Jensen (Loyola University Chicago) leading to a duality theory for the case of relaxed $L^{\infty}$ cost functionals acting on probability measures with prescribed marginals.
BOCIU Lorena
NC State University, United States
Title: Controlling Turbulence in Fluid-Elasticity Interactions (details)
Reducing and controlling turbulence inside the fluid flow in fluid-structure interactions is particularly relevant in the design of small-scale unmanned aircrafts and morphing aircraft wings, and is also of great interest in the medical community (for example, blood flow in a stenosed or stented artery). Existing literature on control problems in fluid-structure interactions is predominantly focused on the assumption of small but rapid oscillations of the solid body, so that the common interface is assumed static. In comparison, we address the issue of minimizing turbulence inside the fluid in the case of a moving boundary interaction between a viscous, incompressible fluid and an elastic body. The PDE model consists of the Navier-Stokes equations coupled with the nonlinear equations of elastodynamics. Due to the strong nonlinearity of the model and the moving domains, the minimization problem requires a combination of tools from optimal control and sensitivity/shape analysis. In this talk, we will discuss the existence of an optimal control and the derivation of the first order necessary optimality conditions.
BOT Radu Ioan
University of Vienna, Austria
Title: Primal-dual algorithms for complexly structured nonsmooth convex optimization problems (details)
In this talk we address the solving of a primal-dual pair of convex optimization problems with complex and intricate structures, by actually solving the corresponding system of optimality conditions, which involves mixtures of linearly composed, Lipschitz single-valued and parallel-sum type monotone operators. The proposed numerical schemes have as common feature the fact that the set-valued maximally monotone operators are processed individually via backward steps, while the single-valued ones are evaluated via explicit forward steps. The performances of the primal-dual algorithms are illustrated by numerical experiments on real-life problems arising in image and video processing, optimal portfolio selection and machine learning.
Universidad Politecnica de Madrid, Espana
Title: Null controllability of coupled systems of PDE's (details)
We present a new strategy for the control of coupled systems of PDE's. The main idea is to write the solutions and controls of the system in series form where each term satisfies a new control problem, still coupled, but that can be written in cascade form. This means that the coupling term appears only in one of the equations and the controllability can be deduced from suitable observability inequalities for the uncoupled equations. The control for the fully coupled system is then obtained combining the controllability of this reduced system with the convergence of the series. We apply this technique to the linear system of thermoelastic plates when we consider two different controls supported in some, possibly different, open sets.
CERNEA Aurelian
University of Bucharest, Romania
Title: Existence results for a class of quadratic integral inclusions (details)
documentclass[12pt]{article} begin{document} title{Existence results for a class of quadratic integral inclusions} author{Aurelian Cernea Faculty of Mathematics and Computer Science, University of Bucharest, Academiei 14, 010014 Bucharest, Romania e-mail:} date{} maketitle We are concerned with the following integral inclusion $$ x(t)in (fx)(t)int_0^tk(t,s)F(s,x(s))ds,quad tin I:=[0,T], $$ where $f:C(I,{mathbf{R}}^n)to C(I,{mathbf{R}}^n)$, $k:Itimes Ito {mathbf{R}}^n$, $F:Itimes {mathbf{R}}^nto mathcal{P}({mathbf{R}}^n)$ is a set-valued map and, for simplicity, by $k(t,s)F(s,x(s))$ we mean the set ${;; vin F(s,x(s))}$ with $<,>$ the scalar product on ${mathbf{R}}^n$. In the case when $F(.,.)$ has convex values and is Carath'{e}odory, using a sort of Leray-Schauder nonlinear alternative for set-valued maps we prove the existence of solutions for the integral inclusion considered. Another existence result is obtained in the case when the set-valued map has non convex values and is lower semicontinuous. The proof is based on the Leray-Schauder alternative for single-valued maps and Bressan-Colombo-Fryszkowski selection theorem. end{document}
Institute of Mathematics and Computer Science of the Academy of Sciences of Moldova, Republic of Moldova
Title: Transvectants and Lyapunov quantities for bidimensional polynomial systems of differential equations with nonlinearities of the fourth degree (details)
\documentclass[10pt,a4paper]{article} \usepackage{amssymb} \usepackage{amsmath} \begin{document} Let us consider the bidimensional polynomial system of differential equations with nonlinearities of the fourth degree \begin{equation} \label{eq:1} {dx \over dt} = P_1(x, y)+P_4(x, y),\quad {dy \over dt} = Q_1(x, y)+Q_4(x, y), \end{equation} where $P_i(x,\ y),\ Q_i(x,\ y)$ are homogeneous polynomials of degree $i$ with real coefficients. The $GL(2, \mathbb{R})$-comitants of the first degree with respect to the coefficients of the system \eqref {eq:1} have the form \begin{equation} \label{eq:2} R_i = P_i(x, y)y-Q_i(x, y)x, \ S_i = {1\over i} \left({{\partial P_i(x, y)}\over {\partial x}}+ {{\partial Q_i(x, y)}\over {\partial y}}\right), \ i=1,4. \end{equation} By using the comitants $R_i$ and $S_i\ (i=1,4)$, system \eqref{eq:1} can be written in the form \begin{equation} \label{eq:3} \dfrac {dx}{dt} = \dfrac {1}{2} \dfrac {\partial R_1} {\partial y} + \dfrac {1}{2} S_1 x + \dfrac {1}{5} \dfrac {\partial R_4} {\partial y} + \dfrac {4}{5} S_4 x, \, \dfrac {dy}{dt} = - \dfrac {1}{2} \dfrac {\partial R_1} {\partial x} + \dfrac {1}{2} S_1 y - \dfrac {1}{5} \dfrac {\partial R_4} {\partial x} + \dfrac {4}{5} S_4 y . \end{equation} Let $f$ and $\varphi$ be polynomials in the coordinates of the vector $(x,y)\in \mathbb{R}^2$ of degrees $r$ and $\rho$, respectively. The polynomial $$ (f,\varphi)^{(k)}={(r-k)!(\rho-k)!\over r!\rho!}\sum_{h=0}^k (-1)^h % \pmatrix{ k \cr h } % C_k^h \binom {k}{h} {\partial^k f\over \partial x^{k-h}\partial y^h} {\partial^k \varphi\over \partial x^h\partial y^{k-h}} $$ is called the {\it transvectant} of the index $k$ of the polynomials $f$ and $\varphi$. Using system \eqref{eq:1} written in the form \eqref{eq:3}, the comitants \eqref{eq:2} and the notion of the transvectant for the system \eqref{eq:1} the recurent formulas for the Lyapunov quantities: $G_8$, $G_{14}$, $G_{20}$, $\dots$, $G_{6m+2}$, $\dots$, where $m \in \mathbb{N^{\ast}}$ were constructed. \end{document}
CSETNEK Ernoe Robert
University of Vienna, Austria
Title: An inertial forward-backward algorithm for the minimization of the sum of two nonconvex functions (details)
We present a forward-backward proximal-type algorithm with inertial/memory effects for minimizing the sum of a nonsmooth function with a smooth one in the nonconvex setting. Every sequence of iterates generated by the algorithm converges to a critical point of the objective function provided an appropriate regularization of the objective satisfies the Kurdyka-Lojasiewicz inequality, which is for instance fulfilled for semi-algebraic functions. We illustrate the theoretical results by considering two numerical experiments: the first one concerns the ability of recovering the local optimal solutions of nonconvex optimization problems, while the second one refers to the restoration of a noisy blurred image.
Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Romania
Title: On the bounded and stabilizing solution of a generalized Riccati differential (details)
\documentclass[a4paper,12pt]{book} \usepackage{amsmath,amsthm,amsfonts} \usepackage{amssymb} \usepackage{palatino} \usepackage[mathscr]{eucal} \textwidth 15cm \textheight 23cm \oddsidemargin 0.7 cm \evensidemargin 0cm \topskip 0cm \headheight 0cm \topmargin 0cm \begin{document} \parindent 0mm \pagestyle{plain} %*************** PLEASE DO NOT REMOVE THIS STAR LINE ************** \newpage \begin{center} \begin{Large} \begin{bf} On the bounded and stabilizing solution of a generalized Riccati differential \\[0.2cm] equation with periodic coefficients arising in connection with a zero sum linear quadratic stochastic differential game \\[.7cm] \end{bf} \end{Large} \begin{large} VASILE DRAGAN\\[0.2cm] {\em Institute of Mathematics "Simion Stoilow" of the Romanian Academy}\\ %{\em of the Romanian Academy}\\ {\em P.O.Box 1-764, RO-014700, Bucharest, Romania}\\ %{\em Bucharest, Romania}\\[0.2cm] {\em}\\[0.4cm] \end{large} \end{center} We consider a system of coupled matrix nonlinear differential equations arising in connection with the solution of a zero sum two players linear quadratic differential game for a system modeled by an Ito differential equation subject to random switching according with a standard homogeneous Markov process with a finite number of state. The system of differential equations under consideration contains as special cases the game theoretic Riccati differential equations arising in the solution of the $H_{\infty}$ control problem from the deterministic and stochastic cases. Among the global solution of the generalized game theoretic Riccati equation, an important role in the construction of the solution of the zero sum two players linear quadratic differential game is played by the so called {\it stabilizing solution}. In this work we present a set of conditions which guarantee the existence and uniqueness of the bounded and stabilizing solution of the Riccati differential equation under consideration. Also, we shall provide a method for numerical computation of this bounded and stabilizing solution. It is worth mentioning that we do not know a priori neither an initial value nor a boundary value of the bounded and stabilizing solution of the Riccati differential equation under investigation. That is why, the numerical methods applicable for the approximation of the solution of a Cauchy problem or of a boundary value problem associated to a differential equation cannot be used to compute the bounded and stabilizing solution of a Riccati differential equation. The bounded and stabilizing solution of the generalized game theoretic Riccati differential equation is obtained as a limit of a sequence of bounded and stabilizing solutions of some Riccati differential equations with defined sign of the quadratic parts. For this kind of Riccati differential equation already exits reliable iterative procedures to obtain the stabilizing solution. \\[0.4cm] % % {\bf References}\\[0.1cm] % % \newcommand\itm[2]{\parbox[t]{1cm}{#1}\parbox[t]{14cm}{#2}\\[1mm] } % \itm{[1]} {V. Dragan: {\em Stabilizing solution of periodic game theoretic Riccati differential equation of stochastic control}, {IMA Journal of Mathematical Control and Information,} doi:10.1093/imamci/dnu026, (2014).} % % % %*************** PLEASE DO NOT REMOVE THIS STAR LINE ************** % % \end{document}
University of Craiova, Romania
Title: On the spectrum of some eigenvalue problems (details)
The goal of this presentation is to emphasize different situations regarding the nature of the spectrum of some eigenvalue problems involving elliptic differential operators. More precisely, we will show that the spectrum of such an eigenvalue problem can be either discrete or continuous or a combination of the above two cases involving a continuous part plus an isolated point.This is a joint work with Mihai Mihailescu and Denisa Stancu-Dumitru.
University of Bologna, Italy
Title: Inverse problems from control theory (details)
Some inverse problems for abstract differential equations are discussed. The motivation comes from relevant equations of interest from control theory.
GAL Ciprian G
Florida International University, Miami, Florida, USA
Title: On reaction-diffusion equations with anomalous diffusion and various boundary conditions (details)
We wish to present recent developments concerning the long term behavior (as time goes to infinity) in terms of finite dimensional global attractors and (global) asymptotic stabilization to steady states of solutions to non-local semi-linear reaction-diffusion equation associated with the fractional Laplace operator on non-smooth domains subject to Dirichlet, fractional Neumann and Robin boundary conditions.
DIEI - Università degli Studi di Cassino e del Lazio Meridionale, Italy
Title: Homogenization of highly oscillating boundaries with strongly contrasting diffusivity (details)
Abstract: I shall discuss a joint work with A. Sili (Département de Mathématiques, Université du Toulon, and Centre de Mathématiques et Informatique, Aix Marseille Université). In this paper, we consider a linear diffusion problem, with strongly contrasting diffusivity, in a medium having highly oscillating boundary. The problem is characterized by two small positive parameters: a parameter $\varepsilon$ describing the periodicity of the oscillating boundary and a parameter $\alpha_\varepsilon$ describing the contrasting diffusivity. As $\varepsilon$ and $\alpha_\varepsilon$ vanish, we pinpoint three different limit regimes depending on ratio $l=\lim\frac{\alpha_\varepsilon}{\varepsilon}$, according to $l=0$, $0
University of Pavia, Italy
Title: Sliding modes for a phase field system (details)
The talk regards the modification of a Caginalp type phase field system obtained by introducing suitable feedback control terms in the equations in order that the trajectories reach a prescribed manifold of the phase space in a finite time and then lie there with a sliding mode. More precisely, two problems are considered. In the first one, the feedback control law is added to the energy balance equation and a linear relationship between temperature and order parameter is forced. In the second case, the modification is inserted in the phase dynamics in order that a prescribed distribution of the order parameter is reached. In both cases, well-posedness and regularity of the solution are discussed and it is shown that the desired sliding actually occurs in a finite time. The results we present regard a recent joint research project with V. Barbu, P. Colli, G. Marinoschi and E. Rocca.
Politecnico di Milano, Italy
Title: Nonlocal Cahn-Hilliard equations (details)
I intend to present some results on nonlocal Cahn-Hilliard equations I have obtained in collaboration with several authors.
Dipartimento di matematica, University of Bologna, Italy
Title: On recostruction of a source term depending on time and space variables in a parabolic mixed problem (details)
We determine a factor depending on both time and one of the spaces variables in a mixed parabolic system in a cylindrical domain. In order to do this, we employ a certain supplementary information, concerning a space-time measurement of the solution.
GUTU Valeriu
Moldova State University, Republic of Moldova
Title: Shadowing pseudo-orbits in set-valued dynamics (details)
We are concerned with dynamical systems, generated by finite families of continuous mappings, not necessarily contractive, in metric spaces, called also Iterated Function Systems (IFS). In case of affine mappings and under suitable cone condition, we localize the maximal compact viable on $Z$ subset and prove the Shadowing property of the IFS on this subset.
Institutul de Matematica Simion Stoilow and Faculty of Mathematics, University of Bucharest, ROmania
Title: Dispersion property for Schr\ (details)
In this talk we analyze the dispersion property of some models involv- ing Schrodinger equations. First we focus on the discrete case and then we present some results on graphs.
Universite Paul Sabatier - Toulouse III, France
Title: Kinetic formulation for vortex vector fields (details)
We will focus on vortex gradient fields of unit-length. The associated stream function solves the eikonal equation, more precisely it is the distance function to a point. We will prove a kinetic formulation characterizing such vector fields in any dimension. This characterization is useful in many variational models such as the study of zero energy states in a Ginzburg-Landau type model.
KIRR Eduard - Wilhelm
University of Illinois, USA
Title: Large Solitary Waves via Global Bifurcation Methods (details)
We will show how the now classical Global Bifurcation Theory can be enhanced by determining the limit points of solitary wave branches at the boundary of the domain inside which the theory applies. From these limit points we can track the branches back into the domain, and, in the examples we have analyzed so far, determine all the branches i.e., all solitary waves regardless of their size.
KRISTALY Alexandru
Babes-Bolyai University, Romania
Title: Gagliardo-Nirenberg inequalities on manifolds: the influence of the curvature (details)
Title: Gagliardo-Nirenberg inequalities on manifolds: the influence of the curvature Abstract: In this talk we discuss the validity of the Gagliardo-Nirenberg inequality (shortly, GN inequality) and its limit cases on Riemannian manifolds. First, when the manifold has non-negative Ricci curvature and the GN inequality holds, we shall provide a sharp, quantitative volume growth of geodesic balls. Second, when the manifold has non-positive sectional curvature, we establish a sharp GN inequality whenever the Cartan-Hadamard conjecture holds (e.g., the dimension of the manifold is 2, 3 or 4).
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Republic of Moldova
Title: Determining the Saddle Points for Antagonistic Positional Games in Markov Decision Processes (details)
A class of stochastic antagonistic positional games for Markov decision processes with average and expected total discounted costs optimization criteria are formulated and studied. Saddle point conditions in the considered class of games that extend saddle point conditions for deterministic parity games are derived. Furthermore algorithms for determining the optimal stationary strategies of the players are proposed and grounded.
"Gheorghe Asachi" Technical Universiy of Iasi, Romania
Title: Positive solutions for a system of singular second-order integral boundary value problems (details)
We investigate the existence of positive solutions of a system of second-order nonlinear differential equations subject to Riemann-Stieltjes integral boundary conditions, where the nonlinearities do not possess any sublinear or superlinear growth conditions and may be singular. In the proof of our main results, we use the Guo-Krasnosel'skii fixed point theorem.
Universitatea Politehnica Bucuresti & Simion Stoilow Institute of Mathematics of the Romanian Academy, Romania
Title: Numerical meshes ensuring uniform observability of 1d waves (details)
In this talk, we build non-uniform numerical meshes for the finite difference and finite element approximations of the 1-d wave equation, ensuring that all numerical solutions reach the boundary, as continuous solutions do, in the sense that the full discrete energy can be observed by means of boundary measurements, uniformly with respect to the mesh-size. The construction of the nonuniform mesh is achieved by means of a concave diffeomorphic transformation of a uniform grid into a non-uniform one, making the mesh finer and finer when approaching the right boundary. For uniform meshes it is known that high-frequency numerical wave packets propagate very slowly without never getting to the boundary. Our results show that this pathology can be avoided by taking suitable non-uniform meshes. This also allows to build convergent numerical algorithms for the approximation of boundary controls of the wave equation.
Université Paul Sabatier - Toulouse 3, France
Title: On some minimization problems in $R^N$: the concentration-compactness principle revisited (details)
We present recent improvements of the concentration-compactness principle and show that they give a new insight in some old minimization problems leading to the existence of solitary waves for nonlinear dispersive equations.
Université Catholique de Louvain, Belgium
Title: Periodic solutions of relativistic-type systems with periodic nonlinearities (details)
The lecture surveys recent results on the multiplicity of periodic solutions of differential systems of the type $$left(frac{u'}{sqrt{1-|u'|^2}}right) + nabla_u V(t,u) = e(t)$$ when the potential $V$ is periodic in each component of $u$ and $e$ has mean value zero over the time period.
University of Craiova & "Simion Stoilow" Institute of Mathematics of the Romanian Academy, Romania
Title: On the asymptotic behavior of some classes of nonlinear eigenvalue problems involving the $p$-Laplacian (details)
The goal of this talk is to present recent results concerning two different PDEs which can be regarded as the limiting equations of some families of nonlinear eigenvalue problems. First, eigenvalue problems involving the $p$-Laplacian and rapidly growing operators in divergence form are studied in an Orlicz-Sobolev setting. An asymptotic analysis of these problems leads to a full characterization of the spectrum of an exponential type perturbation of the Laplace operator. Next, the issue of existence of nonnegative solutions for a class of problems depending on a real parameter and involving the $\infty$-Laplacian is considered. It is shown that nontrivial nonnegative viscosity solutions for this class of problems exist if and only if the parameter is greater than or equal to the reciprocal of the maximum of the distance to the boundary of the domain. This is a joint work with Marian Bocea (Loyola University Chicago).
MOSCO Umberto
Worcester Polytechnic Institute, USA
Title: Time, grids, similarity (details)
We construct certain discrete dynamical systems governed by ODEs on syncronized time-space infinite grids, which give rise asymptotically to filling space attractors. The role of time-space grid syncronization in the description of fast short-range dynamics will also be discuseed
Moldova State University, Republic of Moldova
Title: Singularly perturbed problems for abstract differential equations of second order in Hilbert spaces (details)
Let $H$ and $V$ be two real Hilbert spaces such that $V\subset H$ continuously and densely. Let $A:V=D(A)\subset H\to H$ be a self-adjoint positive definite operator and let $B:D(B)\subset H\to H$ be a nonlinear operator. Consider the following abstract hyperbolic system $$ \left\{\begin{array}{ll} \varepsilon\,u''_{\varepsilon}(t)+\delta u'_{\varepsilon}(t)+ A\,u_{\varepsilon}(t)+B\big(u_{\varepsilon}(t)\big)=f_{\varepsilon}(t),\quad t \in (0,T), \\ u_{\varepsilon}(0)=v_{0\varepsilon},\quad u'_{\varepsilon}(0)=v_{1\varepsilon}.\ \end{array}\right. $$ Under some conditions on operators $A$ and $B$ we study the behavior of solutions $u_\varepsilon$ as $\varepsilon \to 0, \delta \to 0$.
RADU Petronela
University of Nebraska-Lincoln, USA
Title: Oscillational blow-up of traveling solutions in models for suspension bridges (details)
The study of fourth order differential equations has recently intensified in the context of studying the behavior of traveling waves for nonlinear suspension bridges. I will present a blow-up result for the equation [ u^{(4)}+ku''+f(u)=0 ] where $f$ is super linear with $f(u)u>0$ and when $k>0$. Previous work by Gazzola and his collaborators solved the case $kleq 0$. The case $k>0$ is physically significant as it corresponds to $k=c^2$ with $c$ being the speed of propagation of the traveling wave.
RUSU Galina
Moldova State University, Republic of Moldova
Title: Some singularly perturbed Cauchy problems for abstract linear differential equations with positive powers of a positive defined operator (details)
In a real Hilbert space $H$ consider the following Cauchy problem: $$ \left\{ \begin{array}{l} \varepsilon\Big(u''_{\varepsilon}(t)+A_1u_{\varepsilon}(t)\Big)+u'_{\varepsilon}(t)+ A_0u_{\varepsilon}(t)=f_{\varepsilon}(t), \quad t \in (0,T), \\ u_{\varepsilon}(0)=u_{0\varepsilon},\quad u'_{\varepsilon}(0)=u_{1\varepsilon},\ \end{array} \right. \eqno {(P_{\varepsilon})} $$ where $A_i:D(A_i)\subset H\to H$, $i=0,1,$ are two linear self-adjoint operators, $\varepsilon >0$ is a small parameter $(\varepsilon\ll 1)$, $u_{\varepsilon},f_{\varepsilon}: [0,T) \to H$. Supposing that the operator $A_1$ is subordinated to a positive power of the operator $A_0,$ the behavior of solutions $u_\varepsilon$ to the problems ($P_\varepsilon$), when $u_{0\varepsilon}\to u_0,$ $f_{\varepsilon}\to f$ as $\varepsilon \to 0,$ is investigated. We establish a relationship between solutions to the problems ($P_{\varepsilon}$) and the corresponding solution to the following unperturbed problem: $$ \left\{ \begin{array}{l} v'(t)+A_0v(t)=f(t), \quad t\in (0,T),\\ v(0)=u_0. \end{array} \right.\eqno{(P_0)} $$
SATCO Bianca
Stefan cel Mare University of Suceava, Romania
Title: Mild solutions for functional semilinear evolution equations (details)
\documentclass[10pt]{article} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \usepackage{graphicx} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} %TCIDATA{OutputFilter=LATEX.DLL} %TCIDATA{Created=Fri Jan 28 13:39:02 2005} %TCIDATA{LastRevised=Thu Feb 03 17:22:44 2005} %TCIDATA{} %TCIDATA{} %TCIDATA{CSTFile=LaTeX article (bright).cst} \newtheorem{theorem}{Theorem} \newtheorem{acknowledgement}[theorem]{Acknowledgement} \newtheorem{algorithm}[theorem]{Algorithm} \newtheorem{axiom}[theorem]{Axiom} \newtheorem{case}[theorem]{Case} \newtheorem{claim}[theorem]{Claim} \newtheorem{conclusion}[theorem]{Conclusion} \newtheorem{condition}[theorem]{Condition} \newtheorem{conjecture}[theorem]{Conjecture} \newtheorem{corollary}[theorem]{Corollary} \newtheorem{criterion}[theorem]{Criterion} \newtheorem{definition}[theorem]{Definition} \newtheorem{example}[theorem]{Example} \newtheorem{exercise}[theorem]{Exercise} \newtheorem{lemma}[theorem]{Lemma} \newtheorem{notation}[theorem]{Notation} \newtheorem{problem}[theorem]{Problem} \newtheorem{proposition}[theorem]{Proposition} \newtheorem{remark}[theorem]{Remark} \newtheorem{solution}[theorem]{Solution} \newtheorem{summary}[theorem]{Summary} \newenvironment{proof}[1][Proof]{\textbf{#1.} }{\ \rule{0.5em}{0.5em}} %\input{tcilatex} \textwidth 14cm \textheight 21.8cm \begin{document} \title{Mild solutions for functional semilinear evolution equations} \author{Bianca Satco\thanks{Stefan cel Mare University, Faculty of Electrical Engineering and Computer Science, Universitatii 13 - SUCEAVA - ROMANIA ; email:}} \date{} \maketitle %\scriptsize %\noindent } %\maketitle {\noindent {\bf Abstract.} We study the matter of existence of mild solutions for functional semilinear evolution equations with a non-necessarily absolutely integrable function on the right-hand side. We make use of the properties of Kurzweil integrals and of Kurzweil-Stieltjes integrals for operators. \end{document}
SERBAN Calin - Constantin
West University of Timisoara, Romania
Title: Existence results for discontinuous perturbations of singular $\phi$-Laplacian operator (details)
Systems of differential inclusions of the form $$-(\phi(u'))'\in \partial F(t,u), \quad t\in [0,T],$$ where $\phi=\nabla\Phi$, with $\Phi$ strictly convex, is a homeomorphism of the ball $B_a\subset\mathbb{R}^N$ onto $\mathbb{R}^N$, are considered under Dirichlet, periodic and Neumann boundary conditions. Here, $\partial F(t,x)$ stands for the generalized Clarke gradient of $F(t,\cdot)$ at $x\in\mathbb{R}^N$. Using nonsmooth critical point theory, we obtain existence results under some appropriate conditions on the potential $F$. The talk is based on joint work with Petru Jebelean and Jean Mawhin. \smallskip \textbf{Acknowledgements:} The work of the speaker was supported by the strategic grant POSDRU/159/1.5/S/137750, "Project Doctoral and Postdoctoral programs support for increased competitiveness in Exact Sciences research".
Universite de Perpignan, France
Title: Discontinuous control problems and optimality conditions via occupational measures (details)
We present a linearization method for control problems in deterministic and stochastic case. This method allows us to transform a nonlinear control problem with a minimal cost into a maximization of a linear problem over occupational measures. This formulation is very useful because it allows for instance to obtain approximation results for the values ​​functions using Dirac measures. We consider deterministic and stochastic control problems with discontinuous cost. Using the occupation measures we handle a difficult problem: the characterization of semi-continuous value ​​functions. The value function is the generalized viscosity solution for the associated Hamilton-Jacoby-Bellman equation. A dual formulation of the problem is obtained. Naturally, under certain assumptions, the primal value and dual value coincide. This formulation is used to derive optimality conditions. Moreover, we describe examples where this method is used in a theoretical framework as well as into a more applied one.
University of Cergy-Pontoise, France
Title: Global stabilisation for damped-driven conservation laws (details)
We consider a multidimensional conservation law with a damping term and a localised control. Our main result proves that any (non-stationary) solution $u(t,x)$ can be exponentially stabilised in the following sense: for any initial state one can find a control such that the difference between the corresponding solution and the function $u(t)$ goes to zero exponentially fast in an appropriate norm. As a consequence, we prove global exact controllability to solutions of the problem in question. We also establish global approximate controllability to solutions with the help of low-dimensional localised controls.
“Babeș-Bolyai” University, Cluj-Napoca and “Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania
Title: A Baouendi-Grushin type operator in Orlicz-Sobolev spaces and applications to PDEs (details)
We introduce a Baouendi-Grushin operator in the setting of Orlicz-Sobolev spaces and we establish a sharp result regarding the spectrum of this operator. More exactly, we show that the spectrum is continuous. The proofs are based on the critical point theory combined with adequate variational methods. This presentation is a joint work with Mihai Mihăilescu (University of Craiova and “Simion Stoilow” Institute of Mathematics of the Romanian Academy) and Csaba Varga (“Babeș-Bolyai” University).
Purdue University Calumet, USA
Title: On Constrained Wave Propagation (details)
Many important applications lead to hyperbolic systems of differential equations supplemented by constraint equations on infinite domains (e.g., Maxwell’s equations and Einstein’s field equations in various hyperbolic formulations). In general, for the pure Cauchy problem one can prove that the constraints are preserved by the evolution. That is, the solution satisfies the constraints for all time whenever the initial data does. Frequently, the numerical solutions to such evolution problems are computed on artificial space cutoffs because of the necessary boundedness of computational domains. Therefore, well-posed boundary conditions are needed at the artificial boundaries. Moreover, these boundary conditions have to be chosen in such a way that the numerical solution of the cutoff system approximates as best as possible the solution of the original problem on infinite domain, including the preservation of constraints. In this talk, I will present a general technique for finding constrained preserving boundary conditions, and its application to a system of wave equations in a first-order formulation subject to divergence constraints.
University of California, Berkeley, USA
Title: Long time dynamics for water waves (details)
The water wave equation describes the motion of the free surface of an inviscid, incompressible irrorational fluid, moving under the influence of gravity, surface tension, etc. The goal of the talk will be to present several recent ideas and results concerning long time dynamics for such problems.
TKACENKO Alexandra
State University of Moldova, Republic of Moldova
Title: The fractional multi-objective transportation problem of fuzzy type. (details)
\documentclass[11pt, a4paper]{article} \begin{document} \title{The fractional multi-objective transportation problem of fuzzy type.} \author{Tkacenko Alexandra\\ Department of Applied Mathematics, Moldova State University\\ A. Mateevici str., 60, Chisinau, MD--2009, Moldova \\} \date{} \maketitle In the paper is developed an iterative fuzzy programming approach for solving the multi-objective fractional transportation problem of "bottleneck" type [1] with some imprecise data. Minimizing the worst upper bound to obtain an efficient solution which is close to the best lower bound for each objective function iterative, we find the set of efficient solutions for all time levels [3]. The mathematical model of the proposed problem is the follows: \begin{equation} \min Z^{k}=\displaystyle\frac{\sum\limits_{i=1}^{m}\sum\limits_{i=1}^{n}\tilde{c}_{ij}^{k}x_{ij}}{\max\limits_{ij}\{t_{ij}\left| x_{ij}>0\}\right.} \end{equation} \begin{equation} \min Z^{k+1}=\max\limits_{ij}\{ t_{ij}\left|x_{ij}>0\right.\} \end{equation} \begin{equation} \sum\limits_{j=1}^{n}x_{ij}=a_{i}, \, i=1,2,\dots, m;\quad \, \sum\limits_{i=1}^{n} x_{ij}=a_{i}, j=1,2,\dots, n; \end{equation} \begin{equation} x_{ij}\ge 0,\, i=1,2,\dots,m,\, j=1,2,\dots,n,\, k=1,2,\dots ,r. \end{equation} where: $Z^{k}(x)=\left\{Z^{1}(x), Z^{2}(x),\dots, Z^{k}(x) \right\}$ is a vector of $r$ objective functions; $\tilde{c}_{ij}^{k} $ , k=1,2\dots r, i=1,2,\dots m, j=1,2,\dots n are unit costs or other amounts of fuzzy type, $ t_{ij} $ - necessary unit transportation time from source $i$ to destination $j$, $a_{i} $ - disposal at source i, $b_{j} $ -requirement of destination $j$, $x_{ij} $ - amount transported from source $i$ to destination $j$. In order to solve the model (1)-(4) we proposed to reduce it to one of linear type, equivalent in terms of the set of solutions. Since the parameters and coefficients of transportation multi-criteria models have real practical significances such as unit prices, unit costs and many other, all of them are interconnected with the same parameter of variation, which can be calculated by applying of various statistical methods. Thus, the model (1)-(4) can be transformed in one with deterministic type of data. It can be solved using fuzzy techniques: \begin{equation} \mu_{k}(Z^{k}))=\left\{ \begin{array}{ccc}1, \textrm{if } Z^{k}(x)\le L_k\\ \displaystyle\frac{U_k-Z^{k}(x)}{U_k-L_k},\, \textrm{if}, \, L_k
CEREMADE, Universite Paris Dauphine and Institut Universitaire de France (IUF), FRANCE
Title: Mathematical models of vaccination: societal and invididual views (details)
The mathematical models of vaccination is a relatively old subject. Initial works focused mostly on the overall, societal optimums; on the contrary recent works can now treat the more difficult individual reactions. These reactions can be mathematically described in a Mean Field Games framework (introduced by P.L. Lions and J.M. Lasry) as a Nash equilibrium in a game with an infinity of players. We present several recent works on the subject and applications to H1N1 2009/10 vaccination in France along with discussions on the cost-effectiveness of public health interventions.
State University of Moldova, Republic of Moldova
Title: Strategic Games, Information Leaks, Corruption, and Solution Principles (details)
We consider strategic games with rules violated by information leaks (corruption of simultaneity). As a result of corruption, various para/pseudo sequential games appear. The classification of such games is provided on the base of the applicable solution principles. Conditions for solution existence are highlighted, formulated and analysed.
University of Babes-Bolyai, Romania
Title: Symmetry and multiple solutions for certain quasilinear elliptic equations (details)
\documentclass[10pt]{amsart} \begin{document} \title{Symmetry and multiple solutions\\for certain quasilinear elliptic equations} \centerline{ROBERTA FILIPPUCCI, PATRIZIA PUCCI and CSABA VARGA} \begin{abstract} We present some symmetrization results which we apply to the same abstract eigenvalue problem in order to show the existence {\em of three different solutions which are invariant by Schwarz symmetrization}. {In particular, we introduce two different methods in order to prove the existence of multiple symmetric solutions. The first is based on the symmetric version of the Ekeland variational principle and the mountain pass theorem, while the latter consists of an application of a suitable symmetric version of the three critical points theorem due to {\em Pucci} and {\em Serrin}. Using the second method, we are able to improve some recent results of {\em Arcoya and Carmona} and {\em Bonnano and Candito}. The methods we present work also for different types of symmetrization. \end{abstract} \end{document}
University of Reading, United Kingdom
Title: Global bifurcation of steady gravity water waves with critical layers (details)
I will present some recent results on the problem of two-dimensional travelling water waves propagating under the influence of gravity in a flow of constant vorticity over a flat bed. By means of a conformal mapping and an application of Riemann-Hilbert theory, the free-boundary problem is equivalently reformulated as a one-dimensional pseudodifferential equation which involves a modified Hilbert transform and, moreover, has a variational structure. Using the new formulation, existence is established, by means of real-analytic global bifurcation theory, of a family of solutions which includes waves of large amplitude, even in the presence of critical layers in the flow. This is joint work with Adrian Constantin (King's College London, UK) and Walter Strauss (Brown University, USA).
Princeton University, United States
Title: Contrast between Lagrangian and Eulerian analytic regularity properties of Euler equations (details)
We consider the incompressible Euler equations on ${mathbb R}^d$, where $din {2,3}$. We prove that: (a) In Lagrangian coordinates the real-analyticity radius (more generally, the Gevrey-class radius) is conserved, locally in time. (b) In Lagrangian coordinates the equations are well-posed in highly anisotropic spaces, e.g. Gevrey-class regularity in the label a1 and Sobolev regularity in the labels a2,...,ad. (c) In Eulerian coordinates both results (a) and (b) above are false!
Towson University, Towson, Maryland - 21208, U.S.A.
Title: The local equicontinuity of a maximal monotone operator and consequences (details)
The local equicontinuity of an operator $T:Xrightrightarrows X^{*}$ with proper Fitzpatrick function $varphi_{T}$ and defined in a barreled locally convex space $X$ has been shown to hold on the algebraic interior of operatorname*{Pr}_{X}(operatorname*{dom}varphi_{T})$)% footnote{see cite[Theorem 4]{MR3252437}% }. The current note presents direct consequences of the aforementioned result with regard to the local equicontinuity of a maximal monotone operator defined in a barreled locally convex space including a new proof of James's Theorem and the universality of the normal cone in the sum theorem for maximal monotone operators.
IMAR and University of Sussex, Romania and UK
Title: Partial regularity and smooth topology-preserving approximations of rough domains (details)
We consider domains whose boundary can be locally represented as the graph of a continuous function and construct smooth approximations that preserve topological properties (in particular the fundamental group, for instance). The main tool for doing this is a notion of (multivalued) map of "good directions at a point", that is a map that associates to a point in the neighbourhood of the boundary the directions along which the boundary can be locally represented as the graph of a continuous function. We study various properties of the map of good directions and also use it to show that there must be points on the the boundary of the domain, in a neighbourhood of which the domain is in fact smoother, it is locally Lipschitz. This is joint work with John M. Ball.