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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2410.22234 |
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| _version_ | 1866913754661257216 |
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| author | Conti, Monica Galimberti, Pietro Gatti, Stefania Giorgini, Andrea |
| author_facet | Conti, Monica Galimberti, Pietro Gatti, Stefania Giorgini, Andrea |
| contents | We study the Cahn-Hilliard equation with non-degenerate concentration-dependent mobility and logarithmic potential in two dimensions. We show that any weak solution is unique, exhibits propagation of uniform-in-time regularity, and stabilizes towards an equilibrium state of the Ginzburg-Landau free energy for large times. These results improve the state of the art dating back to a work by Barrett and Blowey. Our analysis relies on the combination of enhanced energy estimates, elliptic regularity theory and tools in critical Sobolev spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_22234 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior Conti, Monica Galimberti, Pietro Gatti, Stefania Giorgini, Andrea Analysis of PDEs We study the Cahn-Hilliard equation with non-degenerate concentration-dependent mobility and logarithmic potential in two dimensions. We show that any weak solution is unique, exhibits propagation of uniform-in-time regularity, and stabilizes towards an equilibrium state of the Ginzburg-Landau free energy for large times. These results improve the state of the art dating back to a work by Barrett and Blowey. Our analysis relies on the combination of enhanced energy estimates, elliptic regularity theory and tools in critical Sobolev spaces. |
| title | New results for the Cahn-Hilliard equation with non-degenerate mobility: well-posedness and longtime behavior |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2410.22234 |