Nonlinear degenerate cross-diffusion systems with nonlocal interaction
Analysis of PDEs
2017-10-05 v1
Abstract
We investigate a class of systems of partial differential equations with nonlinear cross-diffusion and nonlocal interactions, which are of interest in several contexts in social sciences, finance, biology, and real world applications. Assuming a uniform "coerciveness" assumption on the diffusion part, which allows to consider a large class of systems with degenerate cross-diffusion (i.e. of porous medium type) and relaxes sets of assumptions previously considered in the literature, we prove global-in-time existence of weak solutions by means of a semi-implicit version of the Jordan-Kinderlehrer-Otto scheme. Our approach allows to consider nonlocal interaction terms not necessarily yielding a formal gradient flow structure.
Cite
@article{arxiv.1710.01653,
title = {Nonlinear degenerate cross-diffusion systems with nonlocal interaction},
author = {M. Di Francesco and A. Esposito and S. Fagioli},
journal= {arXiv preprint arXiv:1710.01653},
year = {2017}
}