This project aims at gathering three teams of mathematicians (ENS Cachan-CMLA, Univ. Paris-Dauphine-CEREMADE, Univ. Paris 6-LJLL) specialized in PDEs and their numerical simulation, and already having an experience in the collaboration with teams working in the sector of biology or medical studies. What we propose here is a detailed study of the modeling and the mathematical/numerical analysis of problems arising from different areas of biology, including cell biology, biological fluids, population dynamics and animal collective behavior.
        The common feature of those problems is the need to examine the qualitative properties and the numerical approximations of systems of PDEs which are specially designed to model them, and which are distinct from any of the systems appearing in physics. Most often, they have features which are specific to the application, like an infinite number of equations for coagulation-fragmentation, or cross diffusions terms for the spatial evolution of intelligent species.
        The methods to be used come from the most recent developments in PDE theory, they include existence of nontrivial remarkable states, entropy/entropy dissipation estimates, linear and nonlinear asymptotic stability, perturbative methods, duality lemmas, computer-aided proofs, time-dependent rescaling, renormalized solutions, etc. Our goal is in particular to extract information from systems which are far from known steady states.

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News

Franco-italian meeting on kinetic theory and singular parabolic equations, March 16-17th 2017

Summer school in Probability and PDE for Biology, July 2016

Research Summer School Mathematical modelling in Biology and Medicine, June 8-17th 2016

SIMBAD: Séminaire itinérant de Mathématiques, Biologie et Applications des Doctorants, May 25th 2016

Second meeting on mathematical modeling and control in epidemic spread, May 24th 2016

Workshop on complex systems of reaction-diffusion, March 24-25th 2016