RIBOT , Magali

Nous nous intéressons dans ce mémoire d'habilitation à diriger les recherches à l'étude de systèmes d'équations aux dérivées partielles afin de modéliser des phénomènes biologiques. Dans la première partie, nous étudions différents systèmes de type hyperbolique pour modéliser le phénomène de chimiotactisme, en s'intéressant particulièrement...

We introduce a new class of finite difference schemes for approximating the solutions to an initial-boundary value problem on a bounded interval for a one dimensional dissipative hyperbolic system with an external source term, which arises as a simple model of chemotaxis. Since the solutions to this problem may converge to non constant...

International audience

International audience

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on...

In this article, we study a one-dimensional hyperbolic quasi-linear model of chemotaxis with a non-linear pressure and we consider its stationary solutions, in particular with vacuum regions. We study both cases of the system set on the whole line $\Er$ and on a bounded interval with no-flux boundary conditions. In the case of the whole line...

We introduce a numerical scheme to approximate a quasi-linear hyperbolic system which models the movement of cells under the influence of chemotaxis. Since we expect to find solutions which contain vacuum parts, we propose an upwinding scheme which handles properly the presence of vacuum and, besides, which gives a good approximation of the...

In this paper we deal with a semilinear hyperbolic chemotaxis model in one space dimension evolving on a network, with suitable transmission conditions at nodes. This framework is motivated by tissue-engineering scaffolds used for improving wound healing. We introduce a numerical scheme, which guarantees global mass densities conservation....

We consider two models which were both designed to describe the movement of eukaryotic cells responding to chemical signals. Besides a common standard parabolic equation for the diffusion of a chemoattractant, like chemokines or growth factors, the two models differ for the equations describing the movement of cells. The first model is based on...

We present in this paper a spatial model describing the growth of a photosynthetic microalgae biofilm. In this model we consider photosynthesis, extracellular matrix excretion, and mortality. These mechanisms are described precisely using kinetic laws that take into account some saturation effects which limit the reaction rates and involve...

We discuss the modelling of interacting populations through pursuit-evasion ---- or attraction-repulsion ---- principles~: preys try to escape chasers, chasers are attracted by the presence of preys. We construct a hierarchy of models, ranging from ODEs systems with finite numbers of individuals of each population, to hydrodynamic systems....

We discuss numerical strategies to deal with PDE systems describing traffic flows, taking into account a density threshold, which restricts the vehicles density in the situation of congestion. These models are obtained through asymptotic arguments. Hence, we are interested in the simulation of approached models that contain stiff terms and...