Stability of parabolic equations in non-cylindrical domains
Fuente:
arXiv
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| Auteur principal: | |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915647739396096 |
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| author | Liu, Lingyang |
| author_facet | Liu, Lingyang |
| contents | This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the $L^\infty$-stability of systems for both nondegenerate and degenerate cases. Unlike in cylindrical domains, solutions to such problems may not exhibit exponential decay. An interesting phenomenon observed is that degeneracy has a positive impact on $L^\infty$-norm estimates for solutions to the system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05783 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Stability of parabolic equations in non-cylindrical domains Liu, Lingyang Analysis of PDEs This paper addresses the stability of a class of parabolic equations in non-cylindrical domains. We investigate the $L^\infty$-stability of systems for both nondegenerate and degenerate cases. Unlike in cylindrical domains, solutions to such problems may not exhibit exponential decay. An interesting phenomenon observed is that degeneracy has a positive impact on $L^\infty$-norm estimates for solutions to the system. |
| title | Stability of parabolic equations in non-cylindrical domains |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.05783 |