Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912607458295808 |
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| author | Chen, Xiuqing Du, Bang Jüngel, Ansgar |
| author_facet | Chen, Xiuqing Du, Bang Jüngel, Ansgar |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_17379 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems Chen, Xiuqing Du, Bang Jüngel, Ansgar Analysis of PDEs 35A02, 35K51, 35K65, 35Q92, 92C17 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. |
| title | Stability and uniqueness of bounded weak solutions to triangular degenerate cross-diffusion systems |
| topic | Analysis of PDEs 35A02, 35K51, 35K65, 35Q92, 92C17 |
| url | https://arxiv.org/abs/2508.17379 |