Courses

Henri Berestycki (Paris EHESS) 

Diffusion phenomena in Mathematical Biology

Abstract: TBA 

Emeric Bouin (Paris Dauphine) 

Transport phenomena in Mathematical Biology

Abstract: TBA 

Diane Peurichard (INRIA Paris) 

Simulation and numerical treatment of PDEs in Mathematical Biology.

Abstract: TBA

Maria José Caceres (Granada) 

Mathematical Models in Neurobiology.

Abstract: TBA

Noemi David (Lyon) 

Singular limits arising in mechanical models of tissue growth

Based on the mechanical viewpoint that living tissues present a fluid-like behaviour, PDE models inspired by fluid dynamics are nowadays well established as one of the main mathematical tools for the macroscopic description of tissue growth. Depending on the type of tissue, these models link the pressure to the velocity field using either Brinkman’s law (visco-elastic models) or Darcy’s law (porous-medium equations (PME)). Moreover, the stiffness of the pressure law plays a crucial role in distinguishing density-based (compressible) models from free boundary (incompressible) problems where saturation of the density holds.
This course aims to analyse how to relate different mechanical models of living tissues through singular limits. In particular, we will address the inviscid limit towards the PME, the incompressible limit from the PME towards Hele-Shaw free boundary problems and their joint limit for equations including convective effects as well as for systems of coupled nonlinear equations. The techniques that will be employed during the course include classical tools in the theory of the PME (Aronson-Bénilan estimate, uniform BV-bounds, energy bounds) as well as techniques that are reminiscent of the theory of gradient flows, such as, for instance, the energy dissipation inequality (EDI) formulation.

Nicolas Vauchelet (Paris Nord) 

Mathematical models in population dynamics: applications in agroecology
Abstract: TBA