The Eighth Congress of Romanian Mathematicians

Posters

I. Algebra and Number Theory

II. Algebraic, Complex and Differential Geometry and Topology

III. Real and Complex Analysis, Potential Theory

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

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

VI. Probability, Stochastic Analysis, and Mathematical Statistics

VII. Mechanics, Numerical Analysis, Mathematical Models in Sciences

VIII. Theoretical Computer Science, Operations Research and Mathematical Programming

IX. History and Philosophy of Mathematics

Ordinary and Partial Differential Equations, Variational Methods, Optimal Control

(this list is in updating process)

1.
ARAMA Bianca - Elena
"Alexandru Ioan Cuza" University of Iasi, Romania
Title: The cost of approximate controllability and an unique continuation result at initial time for the Ginzburg-Landau equation (details)
Abstract:
\documentclass[12pt]{article}% \usepackage[english]{babel} \usepackage{amsmath} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{graphicx}% \setcounter{MaxMatrixCols}{30} %TCIDATA{OutputFilter=latex2.dll} %TCIDATA{Version=5.50.0.2890} %TCIDATA{LastRevised=Saturday, June 20, 2015 11:37:42} %TCIDATA{} %TCIDATA{} %TCIDATA{BibliographyScheme=Manual} %BeginMSIPreambleData \providecommand{\U}[1]{\protect\rule{.1in}{.1in}} %EndMSIPreambleData \setlength{\voffset}{-15mm} \setlength{\hoffset}{-12mm} \setlength{\textwidth}{165mm} \setlength{\textheight}{230mm} \begin{document} %%%%%%%%%%%%%%%%% Sample %%%%%%%%%%%%%%%%%%% \noindent THE EIGHTH CONGRES OF ROMANIAN MATHEMATICIANS \newline{\small June 26- July 1, 2015, Ia\c{s}i, Romania} \vskip 7mm \begin{center} {\Large \textsc{The cost of approximate controllability and an unique continuation result at initial time for the Ginzburg-Landau equation}} \newline \vskip 4mm \textsc{Bianca-Elena ~ARAM\u{A}}\newline \vskip1mm \textit{"Alexandru Ioan Cuza" University, \newline Ia\c{s}i, Romania} \newline{\small e-mail: bianca.arama@student.uaic.ro} \end{center} \bigskip We reconsider the Carleman inequalities for the Ginzburg-Landau equation obtained by Rosier and Zhang and we focus on determining precise estimates for the constants involved, i.e., the explicit dependence on $T$, where $\left[ 0,T\right]$ is the maximum interval of time we consider for the systems. We then study the cost of approximate controllability for the linearized equation, i.e., of the minimal norm of a control needed to steer the system in a $\varepsilon$-neighborhood of a given target. In order to obtain explicit bounds of the cost of approximate controllability, we first have to obtain sharp bounds on the cost of controlling to zero. The key point in proving the cost of approximate controllability is to understand how observability inequalities may be used to obtain sharper results on the coercivity of the functional $J$. Of course, sharp coercivity estimates yield sharp upper bounds on the norms of the minimizer.Another interesting consequence of the explicit dependence of the constants in Carleman estimates is an unique continuation result at initial time. \end{document}
2.
BOTEZAT Sorin
Al. I. Cuza University of Iasi, Romania
Title: Banach fixed point principle for multifunctions with contracting orbits (details)
Abstract:
We prove an extension to multivalued mapping of the Banach fixed point principle which preserves most of the conclusions of the original and, in particular, the unicity of the fixed point.
3.
ISAIA Florin
Transilvania University of Brasov, Romania
Title: Non-existence results of higher-order regular solutions for the p(x)-Laplacian (details)
Abstract:
\documentclass[english, 12pt]{article} \usepackage{babel} \usepackage{amssymb} \usepackage{amsmath} \usepackage[margin=1in]{geometry} \begin{document} \title{Non-existence results of higher-order regular solutions for the $p\left(x\right)$-Laplacian} \author{Florin Isaia$^1$} \date{} \maketitle \thanks{ $^1$Transilvania University of Brasov, Department of Mathematics and Computer Science, 50 Iuliu Maniu St, 500091 Brasov, Romania, E-mail: florin.isaia@unitbv.ro} \section*{Abstract} This talk is devoted to present several non-existence results for higher-order regular solutions to the following nonlinear Dirichlet problem $\left\{ \begin{array}{l} -\Delta_{p\left(x\right)} u=d\left(x\right)f\left(u\right)\quad\textup{in}\ \Omega,\\ \left.u\right|_{\partial\Omega}=0, \end{array} \right.$ where $\Omega$ is a smooth bounded open set in $\mathbb{R}^n$, $n\geq 2$, $p:\overline{\Omega}\rightarrow\mathbb{R}$ is a Lipschitz function with $\min_{x\in\overline{\Omega}}p\left(x\right)>1$, $d\in W^{1,h\left(\cdot\right)}\left(\Omega\right)$ with $h:\Omega\rightarrow\left[1,\infty\right)$ log-H\"{o}lder continuous, $f:\mathbb{R}\rightarrow\mathbb{R}$ is a Borel measurable and locally Lebesgue integrable function. These results are subjected to the following natural principle: the stronger (respectively weaker) are the assumptions on the given data $f$, the larger (respectively smaller) is the variable exponent Sobolev space $W^{m,q\left(\cdot\right)}\left(\Omega\right)$ in which no nontrivial strong solutions can be found. To do this, we use some recent developments on superposition operators between higher-order Sobolev spaces. \end{document}
4.
KIZILBUDAK CALISKAN Seda
Yildiz Technical University, Turkey
Title: Calculated of regularized trace of a fourth order regular differential equation (details)
Abstract:
We shall obtain a formula for the regularized trace of a fourth order regular differential equation
5.
MUNTEANU Laura
State University of New York at Oneonta, U.S.A.
Title: An Algorithm for Generating Maximal Simulation Relations in Geometric Control Theory (details)
Abstract:
Abstract: "A relatively recent problem in geometric control theory is the study of simulation relations between nonlinear control systems. In this presentation, we introduce an algorithm for generating simulation relations between certain nonlinear control systems that are affine in inputs and disturbances, and prove that, under appropriate conditions, the algorithm leads to a maximal simulation relation."
6.
NEGRESCU Alexandru
Universitatea Politehnica Bucuresti, Romania
Title: Controllability for the vibrating string equation with Neumann boundary conditions (details)
Abstract:
In this paper we study the controllability in $T=\pi$ for the vibrating string equation with Neumann boundary conditions using the moment problem approach.
7.
OMAR Benniche
Department of Mathematics, Energy and Smart Systems Laboratory (L.E.S.I) Khemis Miliana University, 442500, Algeria, Algeria
Title: Approximate viability on graphs (details)
Abstract:
Let $X$ be a real Banach space and $I \subset \mathbb{R}$ a nonempty and bounded interval. Let $K: I\rightsquigarrow X$ be a multi-function with the graph $\mathcal{K}$. In this talk we present some results concerning approximate viabiliy for the graph $\mathcal{K}$ with respect to the quasi-autonomous semilinear differential inclusion $x^{\prime}(t)\in A x(t)+ F( t,x(t))$ where $A: D(A)\subset X \rightarrow X$ is the infinitesimal generator of a $C_{0}$-semigroup and $F:I\times X\rightsquigarrow X$ is a given multi-function. As applications, we give some results concerning Lipshitz regularity of the solution set and a relaxation result for $x^{\prime}(t)\in A x(t)+ F( t,x(t))$
8.
OZCUBUKCU Zerrin
Yildiz Technical University, Turkey
Title: Calculated the regularized trace of a fourth order regular differential equation (details)
Abstract:
We shall obtain a formula for the regularized trace of a fourth order regular differential equation