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

Kinetic and Parabolic equations, Applications in Physics and Biology, June 24th 2015

One-day workshop on parabolic equations and their applications to life sciences, May 27th 2014

Kickoff day, March 17th 2014