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Liste des exposés

I. Nouvelles tendances en mécanique des fluides

II. Problèmes à frontière libre

III. Modèles mathèmatiques et méthodes numériques en mécanique des milieux continus

VI. Analyse et contrôle des EDP

VIII. Analyse non-lisse et optimisation

(cette liste est en processus d'actualisation)

**List des exposés**

1.

ANITA Sebastian sanita@uaic.ro

Faculty of Mathematics, Al.I. Cuza University of Iasi, Romania

Titre: REGIONAL CONTROL FOR SOME SPATIALLY STRUCTURED POPULATIONS (details)**Résumé:**

We present some control problems related to spatially structured population dynamics. We discuss relevant optimal control problems and stabilization problems for internal controls. A special attention is given to the geometry of the support of the optimal control and of the stabilizing control. The problem of finding the optimal position of the support of the control is faced as well.

Faculty of Mathematics, Al.I. Cuza University of Iasi, Romania

Titre: REGIONAL CONTROL FOR SOME SPATIALLY STRUCTURED POPULATIONS (details)

We present some control problems related to spatially structured population dynamics. We discuss relevant optimal control problems and stabilization problems for internal controls. A special attention is given to the geometry of the support of the optimal control and of the stabilizing control. The problem of finding the optimal position of the support of the control is faced as well.

2.

BADRALEXI Irina irina.badralexi@gmail.com

Univeristatea Politehnica din Bucuresti, Romania

Titre: Periodic solutions in a DDE model (details)**Résumé:**

The mathematical model we study describes a blood cell disorder on the myeloid cell line through a system of DDEs (delay-differential equations). As oscillatory behaviors occur naturally in biological phenomena, we investigate the existence of periodic solutions.

Univeristatea Politehnica din Bucuresti, Romania

Titre: Periodic solutions in a DDE model (details)

The mathematical model we study describes a blood cell disorder on the myeloid cell line through a system of DDEs (delay-differential equations). As oscillatory behaviors occur naturally in biological phenomena, we investigate the existence of periodic solutions.

3.

BEZNEA Lucian lucian.beznea@imar.ro

Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, and University of Bucharest, Faculty of Mathematics and Computer Science, Romania

Titre: Branching processes associated with Neumann nonlinear semi flows (details)**Résumé:**

We emphasize two branching processes related to a nonlinear Neumann boundary value problem. First, using an associated measure-valued branching Markov process, we give a probabilistic representation of the solution of the parabolic problem associated with such a problem, where the boundary condition has a nonlinear pseudo monotone branching mechanism term. The branching occurs on the measures having non-zero traces on the boundary of the open set, with the behavior of a second branching process, a superprocess, having as spatial motion the process on the boundary associated to the reflected Brownian motion. The talk is based on a joint work with Viorel Barbu.

Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest, and University of Bucharest, Faculty of Mathematics and Computer Science, Romania

Titre: Branching processes associated with Neumann nonlinear semi flows (details)

We emphasize two branching processes related to a nonlinear Neumann boundary value problem. First, using an associated measure-valued branching Markov process, we give a probabilistic representation of the solution of the parabolic problem associated with such a problem, where the boundary condition has a nonlinear pseudo monotone branching mechanism term. The branching occurs on the measures having non-zero traces on the boundary of the open set, with the behavior of a second branching process, a superprocess, having as spatial motion the process on the boundary associated to the reflected Brownian motion. The talk is based on a joint work with Viorel Barbu.

4.

BOUIN Emeric bouin@ceremade.dauphine.fr

CEREMADE - Université Paris-Dauphine, France

Titre: Propagation in structured models from biology. (details)**Résumé:**

In this talk, we are interested in biological invasions for which structured models are needed to provide an accurate description of its qualitative features. This is for example the case for migration of bacterial colonies, or for the impressive cane toads invasions in Australia. We will discuss qualitative and quantitative results for two models inspired by these biological issues.

CEREMADE - Université Paris-Dauphine, France

Titre: Propagation in structured models from biology. (details)

In this talk, we are interested in biological invasions for which structured models are needed to provide an accurate description of its qualitative features. This is for example the case for migration of bacterial colonies, or for the impressive cane toads invasions in Australia. We will discuss qualitative and quantitative results for two models inspired by these biological issues.

5.

BUONOMO Bruno buonomo@unina.it

University of Naples Federico II, Italy

Titre: Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans (details)**Résumé:**

In the last few years, new experimental evidences concerning malaria transmission have been reported. We show how these new aspects may be incorporated in classical malaria models. In particular, we develop and analyse a deterministic population-based ordinary differential equation of malaria transmission to consider the impact of three common assumptions of malaria models: (i) malaria infection does not change the attractiveness of humans to mosquitoes; (ii) exposed mosquitoes (infected with malaria but not yet infectious to humans) have the same biting rate as susceptible mosquitoes; and (iii) mosquitoes infectious to humans have the same biting rate as susceptible mosquitoes. The new models are analysed by using bifurcation theory and optimal control. The biological implications of the analytical results are discussed. This research is a joint work with Nakul Chitnis (Swiss Tropical and Public Health Institute) and Hamadjam Abboubakar (UIT--University of Ngaoundere, Cameroon).

University of Naples Federico II, Italy

Titre: Modelling the effects of malaria infection on mosquito biting behaviour and attractiveness of humans (details)

In the last few years, new experimental evidences concerning malaria transmission have been reported. We show how these new aspects may be incorporated in classical malaria models. In particular, we develop and analyse a deterministic population-based ordinary differential equation of malaria transmission to consider the impact of three common assumptions of malaria models: (i) malaria infection does not change the attractiveness of humans to mosquitoes; (ii) exposed mosquitoes (infected with malaria but not yet infectious to humans) have the same biting rate as susceptible mosquitoes; and (iii) mosquitoes infectious to humans have the same biting rate as susceptible mosquitoes. The new models are analysed by using bifurcation theory and optimal control. The biological implications of the analytical results are discussed. This research is a joint work with Nakul Chitnis (Swiss Tropical and Public Health Institute) and Hamadjam Abboubakar (UIT--University of Ngaoundere, Cameroon).

6.

CHOQUET Catherine cchoquet@univ-lr.fr

Lab. MIA, université de La Rochelle, France

Titre: New approach for the tracking of fluid displacement in stratified flows (details)**Résumé:**

We consider a fluid displacement problem in a bounded domain. We focus on a setting where the fluids \emph{tend} to separate into two layers around a transition zone and where the displacement is highly constrained by its environment. A typical example is the salinization of a coastal aquifer. We take into account the layered structure with a sharp interfaces model where the difficulty of the analysis of free boundaries is somehow hidden by an upscaling procedure. We superimpose a three-dimensional phase-field model for closing the problem, thus re-injecting in a new way the realism of diffuse interfaces models but without the usual Fick's assumption. coupling of the phase-field model with the upscaled conservation equations avoids the classical weakness of some phase-field solutions: non-conserved fields. We thus do not need to consider more complex phase-field models, such as for instance Cahn-Hilliard variant with degenerate mobility and logarithmic terms in the free energy. We neither have to use a nonlocal equation with a time or a space-time dependent Lagrange multiplier to enforce conservation of mass. For the mathematical analysis we introduce a new framework which is quite comparable to the one of renormalized solutions. But it is based on an alternative variational formulation, focusing on the structural weakness of the problem. Some numerical illustrations will be provided.

Lab. MIA, université de La Rochelle, France

Titre: New approach for the tracking of fluid displacement in stratified flows (details)

We consider a fluid displacement problem in a bounded domain. We focus on a setting where the fluids \emph{tend} to separate into two layers around a transition zone and where the displacement is highly constrained by its environment. A typical example is the salinization of a coastal aquifer. We take into account the layered structure with a sharp interfaces model where the difficulty of the analysis of free boundaries is somehow hidden by an upscaling procedure. We superimpose a three-dimensional phase-field model for closing the problem, thus re-injecting in a new way the realism of diffuse interfaces models but without the usual Fick's assumption. coupling of the phase-field model with the upscaled conservation equations avoids the classical weakness of some phase-field solutions: non-conserved fields. We thus do not need to consider more complex phase-field models, such as for instance Cahn-Hilliard variant with degenerate mobility and logarithmic terms in the free energy. We neither have to use a nonlocal equation with a time or a space-time dependent Lagrange multiplier to enforce conservation of mass. For the mathematical analysis we introduce a new framework which is quite comparable to the one of renormalized solutions. But it is based on an alternative variational formulation, focusing on the structural weakness of the problem. Some numerical illustrations will be provided.

7.

CRUCEANU Stefan - Gicu stefan.cruceanu@ima.ro

"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of ROMANIAN ACADEMY, Romania

Titre: Riemann Problem for Shallow Water Equations with Discontinuous Porosity (details)**Résumé:**

We investigate the existence of the solution of the Riemann Problem for a simplified water flow model on a vegetated surface -- system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems it is necessary to introduce a family of paths which connect the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical arguments. We provide the structure of the solution for such Riemann Problems. Finally, we present some numerical solutions.

"Gheorghe Mihoc-Caius Iacob" Institute of Mathematical Statistics and Applied Mathematics of ROMANIAN ACADEMY, Romania

Titre: Riemann Problem for Shallow Water Equations with Discontinuous Porosity (details)

We investigate the existence of the solution of the Riemann Problem for a simplified water flow model on a vegetated surface -- system of shallow water type equations. It is known that the system with discontinuous topography is non-conservative even if the porosity is absent. A system with continuous topography and discontinuous porosity is also non-conservative. In order to define Riemann solution for such systems it is necessary to introduce a family of paths which connect the states defining the Riemann Problem. We focus our attention towards choosing such a family based on physical arguments. We provide the structure of the solution for such Riemann Problems. Finally, we present some numerical solutions.

8.

DIMITRIU Gabriel dimitriu.gabriel@gmail.com

Department of Mathematics and Informatics, University of Medicine and Pharmacy "Grigore T. Popa" Iasi, Romania

Titre: Data assimilation using low-rank Kalman filtering (details)**Résumé:**

Understanding the complex dynamics of large systems for which limited, noisy observations are available represents a fundamental and recurring scientific problem. A key stage in such analyses involves data assimilation. The Kalman filtering has become a powerful framework for data assimilation and may be considered the canonical method for solving this kind of problems. This method provides a conceptually simple recursive framework for online Bayesian inference in the context of linear and Gaussian dynamics and observation processes. Furthermore, the Kalman filtering serves as the underlying computational instrument in a wide diversity of non-Gaussian and nonlinear statistical models. This talk presents several computational issues for the data assimilation problem applied to a 2D air pollution model using several low-rank Kalman filters. The low-rank filters are either based on factorizations of the covariance matrix, or approximation of statistics from a finite ensemble. The performance of such filters is investigated with respect to different scenarios defined by the positions of the observation/emission points and the mean pollution rates inside the assimilation domain.

Department of Mathematics and Informatics, University of Medicine and Pharmacy "Grigore T. Popa" Iasi, Romania

Titre: Data assimilation using low-rank Kalman filtering (details)

Understanding the complex dynamics of large systems for which limited, noisy observations are available represents a fundamental and recurring scientific problem. A key stage in such analyses involves data assimilation. The Kalman filtering has become a powerful framework for data assimilation and may be considered the canonical method for solving this kind of problems. This method provides a conceptually simple recursive framework for online Bayesian inference in the context of linear and Gaussian dynamics and observation processes. Furthermore, the Kalman filtering serves as the underlying computational instrument in a wide diversity of non-Gaussian and nonlinear statistical models. This talk presents several computational issues for the data assimilation problem applied to a 2D air pollution model using several low-rank Kalman filters. The low-rank filters are either based on factorizations of the covariance matrix, or approximation of statistics from a finite ensemble. The performance of such filters is investigated with respect to different scenarios defined by the positions of the observation/emission points and the mean pollution rates inside the assimilation domain.

9.

GABRIEL Pierre pierre.gabriel@uvsq.fr

Université de Versailles, France

Titre: A Hamilton-Jacobi equation for subdiffusive motion (details)**Résumé:**

The molecules moving in the cytoplasm of a cell exhibit experimentally a subdiffusive behavior, meaning that their mean-square displacement grows sublinearly with respect to time. This can be modeled at a mesoscopic scale by a continuous time random walk, leading to a structured partial differential equation of the renewal type with jumps. We study the large scale hyperbolic limit of this equation through a Hopf-Cole transformation. We prove the convergence to the viscosity solution of a Hamilton-Jacobi equation.

Université de Versailles, France

Titre: A Hamilton-Jacobi equation for subdiffusive motion (details)

The molecules moving in the cytoplasm of a cell exhibit experimentally a subdiffusive behavior, meaning that their mean-square displacement grows sublinearly with respect to time. This can be modeled at a mesoscopic scale by a continuous time random walk, leading to a structured partial differential equation of the renewal type with jumps. We study the large scale hyperbolic limit of this equation through a Hopf-Cole transformation. We prove the convergence to the viscosity solution of a Hamilton-Jacobi equation.

10.

GEORGESCU Paul v.p.georgescu@gmail.com

Department of Mathematics and Computer Science, Technical University of Iasi, Romania

Titre: On a HIV transmission model with two high risk groups (details)**Résumé:**

We propose a compartmental model for HIV transmission with two high risk groups, female sex workers (SWs) and male injectable drug users (IDUs), and a non high-risk group of male drug-free clients (DFCs). Two transmission routes are accounted for: needle sharing between IDUs and commercial sex between SWs and IDUs or DFCs, three compartments being considered for each group depending on disease stage. For this model, Lyapunov functionals are constructed by means of the graph theoretic approach laid out in Guo, Li and Shuai [1], the global stability of the disease-free and endemic equilibria, respectively, being then obtained via Lyapunov-LaSalle principle in terms of a threshold parameter. [1] H. Guo, M.Y. Li, Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72: 261-279, 2012.

Department of Mathematics and Computer Science, Technical University of Iasi, Romania

Titre: On a HIV transmission model with two high risk groups (details)

We propose a compartmental model for HIV transmission with two high risk groups, female sex workers (SWs) and male injectable drug users (IDUs), and a non high-risk group of male drug-free clients (DFCs). Two transmission routes are accounted for: needle sharing between IDUs and commercial sex between SWs and IDUs or DFCs, three compartments being considered for each group depending on disease stage. For this model, Lyapunov functionals are constructed by means of the graph theoretic approach laid out in Guo, Li and Shuai [1], the global stability of the disease-free and endemic equilibria, respectively, being then obtained via Lyapunov-LaSalle principle in terms of a threshold parameter. [1] H. Guo, M.Y. Li, Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72: 261-279, 2012.

11.

HALANAY Andrei halanay@mathem.pub.ro

University Politehnica of Bucharest, Romania

Titre: A complex model for cell evolution in hematological diseases incorporating treatment, competition and the action of the immune system (details)**Résumé:**

A delay differential equations model is used for the evolution of healthy and leukemic cells under the action of the immune system . Two types of healthy and leukemic cells, short-term stem-like and mature, are considered in competition. Treatment effects are present through functions that depend on the drug concentration in the plasmatic compartment and in some other tissues. Equilibria are determined and their stability is investigated.

University Politehnica of Bucharest, Romania

Titre: A complex model for cell evolution in hematological diseases incorporating treatment, competition and the action of the immune system (details)

A delay differential equations model is used for the evolution of healthy and leukemic cells under the action of the immune system . Two types of healthy and leukemic cells, short-term stem-like and mature, are considered in competition. Treatment effects are present through functions that depend on the drug concentration in the plasmatic compartment and in some other tissues. Equilibria are determined and their stability is investigated.

12.

LITCANU Gabriela glitcanu@yahoo.com

Institute of Mathematics "Octav Mayer" Iasi, Romania

Titre: Mathematical modelling of the immune response (details)**Résumé:**

The main function of the immune system is to prevent or limit the infection. Despite the complexity of the immune responses, in the last decades, several mathematical models have been proposed to describe the interaction between the immune system and the target population (different types of invasive cells). We intend to discuss the advantages or disadvantages of some of such modelling approaches. We also present a mathematical model in order to address some of the questions that arise regarding the answer mechanisms of the immune response to a target invasive cells population.

Institute of Mathematics "Octav Mayer" Iasi, Romania

Titre: Mathematical modelling of the immune response (details)

The main function of the immune system is to prevent or limit the infection. Despite the complexity of the immune responses, in the last decades, several mathematical models have been proposed to describe the interaction between the immune system and the target population (different types of invasive cells). We intend to discuss the advantages or disadvantages of some of such modelling approaches. We also present a mathematical model in order to address some of the questions that arise regarding the answer mechanisms of the immune response to a target invasive cells population.

13.

LUPASCU Oana oana.lupascu@imar.ro

Institut de Mathematiques Appliquees de l'Academie Roumaine, Bucarest, Roumanie

Titre: Branching properties for measure-valued Markov process and applications (details)**Résumé:**

We present results on the construction and path regularity of the measure-valued branching processes. As applications we give a probabilistic numerical approach for a non-linear Dirichlet problem of a branching process and we emphasize branching properties on several spaces of measures, occurring in a construction of the fragmentation processes and in a model for the fragmentation phase of an avalanche.

Institut de Mathematiques Appliquees de l'Academie Roumaine, Bucarest, Roumanie

Titre: Branching properties for measure-valued Markov process and applications (details)

We present results on the construction and path regularity of the measure-valued branching processes. As applications we give a probabilistic numerical approach for a non-linear Dirichlet problem of a branching process and we emphasize branching properties on several spaces of measures, occurring in a construction of the fragmentation processes and in a model for the fragmentation phase of an avalanche.

14.

PETCU Madalina Madalina.Petcu@math.univ-poitiers.fr

University of Poitiers, France

Titre: Etude théorique et numérique sur les équations Cahn-Hilliard-Navier-Stokes visqueuses avec des conditions aux bords dynamiques (details)**Résumé:**

Le but de l'exposé est de présenter des résultats théoriques et numériques sur les équations de Cahn-Hilliard-Navier-Stokes visqueuses avec des conditions aux bords dynamiques. On commence par presenter des résultats sur l'existence, l'unicité et la régularité des solutions pour le modèle. Ensuite nous proposons une discrétisation de type éléments finis et nous montrons la convergence du schéma proposé. On propose après une discrétisation en temps et en espace et on montre la stabilité et la convergence du schéma proposé. study the convergence of the approximate scheme. We also prove the stability and convergence of a fully discretized scheme, obtained using the semi-implicit Euler scheme applied to the space semi-discretization proposed previously. Nu- merical simulations are also presented to illustrate the theoretical results.

University of Poitiers, France

Titre: Etude théorique et numérique sur les équations Cahn-Hilliard-Navier-Stokes visqueuses avec des conditions aux bords dynamiques (details)

Le but de l'exposé est de présenter des résultats théoriques et numériques sur les équations de Cahn-Hilliard-Navier-Stokes visqueuses avec des conditions aux bords dynamiques. On commence par presenter des résultats sur l'existence, l'unicité et la régularité des solutions pour le modèle. Ensuite nous proposons une discrétisation de type éléments finis et nous montrons la convergence du schéma proposé. On propose après une discrétisation en temps et en espace et on montre la stabilité et la convergence du schéma proposé. study the convergence of the approximate scheme. We also prove the stability and convergence of a fully discretized scheme, obtained using the semi-implicit Euler scheme applied to the space semi-discretization proposed previously. Nu- merical simulations are also presented to illustrate the theoretical results.

**Participants**

1.

MILISIC Vuk milisic@math.univ-paris13.fr

CNRS/Laboratoire Analyse, Géométrie et Applications, Univ. P13, France

CNRS/Laboratoire Analyse, Géométrie et Applications, Univ. P13, France