Antoine Zurek, Université de Technologie de Compiègne
From Greg McCracken
This recording is in the process of being subtitled. We aim to have edited captions available within 2 weeks of publishing.
Title: Design and analysis of finite-volume schemes for a class of cross-diffusion systems
Abstract: In this talk we will present an implicit Euler finite-volume scheme for an n-species population cross-diffusion system of Shigesada-Kawasaki-Teramoto (SKT) type. At the continuous level this system admits a formal gradient-flow or entropy structure which allows to prove the existence of nonnegative global weak solutions in time. Our main goal is to preserve this structure at the discrete level. In this aim our key idea is to consider a suitable mean of the mobilities in such a way that a discrete chain rule is fulfilled and a discrete analog of the entropy inequality holds. Then we are able to pove the existence of nonnegative solutions to the scheme and its convergence. Furthermore we will explain how our approach can be extended to a more general class of cross-diffusion systems satisfying some structural conditions.