Weak-strong uniqueness for general cross-diffusion systems with volume filling

Maria Heitzinger; Ansgar Jüngel

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arXiv · 2509.25978

Weak-strong uniqueness for general cross-diffusion systems with volume filling

Maria Heitzinger·Ansgar Jüngel

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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.

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Maria Heitzinger, Ansgar Jüngel. 2025-09-30. Weak-strong uniqueness for general cross-diffusion systems with volume filling. https://arxiv.org/abs/2509.25978

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