Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems
Analysis of PDEs
2025-09-29 v2
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 method, and carefully combining various estimations.
Cite
@article{arxiv.2508.17379,
title = {Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems},
author = {Xiuqing Chen and Bang Du and Ansgar Jüngel},
journal= {arXiv preprint arXiv:2508.17379},
year = {2025}
}