Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems
Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Chen, Xiuqing, Du, Bang, Jüngel, Ansgar
Language: English
Subfield: Modeling and Simulation
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7077974519
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