Weak-strong uniqueness for general cross-diffusion systems with volume filling
Abstract
The weak-strong uniqueness of solutions to a broad class of cross-diffusion systems with volume filling is established. In general, the diffusion matrices are neither symmetric nor positive definite. This issue is overcome by supposing that the equations possess a Boltzmann-type entropy structure, which ensures the existence of bounded weak solutions. In this framework, general conditions on the mobility matrix are identified that allow for the proof of the weak-strong uniqueness property by means of the relative entropy method. The core idea consists in analyzing an augmented mobility matrix that is positive definite only on a specific subspace. Several examples that meet the required assumptions are provided, together with a discussion on possible extensions.
Cite
@article{arxiv.2509.25978,
title = {Weak-strong uniqueness for general cross-diffusion systems with volume filling},
author = {Maria Heitzinger and Ansgar Jüngel},
journal= {arXiv preprint arXiv:2509.25978},
year = {2025}
}