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arXiv · 2508.17379

Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems

Xiuqing Chen·Bang Du·Ansgar Jüngel
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Abstract

The continuous dependence on the initial data and consequently the uniqueness of bounded weak solutions to a class of triangular reaction-cross-diffusion equations is shown. The class includes two-species doubly degenerate equations for nutrient taxis models describing the response of bacteria to nutrient conditions. The key difficulty is the lack of a gradient bound for the difference of the first component of the solution, due to the degeneracy. This issue is overcome by assuming a nonstandard Lipschitz-type condition, applying the $H^{-1}$ method, and carefully combining various estimations.

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Xiuqing Chen, Bang Du, Ansgar Jüngel. 2025-08-24. Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems. https://arxiv.org/abs/2508.17379

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