Strong solutions and weak-strong stability in a system of cross-diffusion equations
Analysis of PDEs
2019-07-25 v3
Abstract
Proving the uniqueness of solutions to multi-species cross-diffusion systems is a difficult task in the general case, and there exist very few results in this direction. In this work, we study a particular system with zero-flux boundary conditions for which the existence of a weak solution has been proven in [Ehrlacher2017]. Under additional assumptions on the value of the cross-diffusion coefficients, we are able to show the existence and uniqueness of strong solutions. The proof relies on the use of an appropriate approximation and a fixed-point argument. In addition, a weak-strong stability result is obtained for this system in dimension one.
Keywords
Cite
@article{arxiv.1812.10711,
title = {Strong solutions and weak-strong stability in a system of cross-diffusion equations},
author = {Judith Berendsen and Martin Burger and Virginie Ehrlacher and Jan-Frederik Pietschmann},
journal= {arXiv preprint arXiv:1812.10711},
year = {2019}
}