Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2019
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| _version_ | 1866911805864935424 |
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| author | Lopes, Pedro T. P. Roidos, Nikolaos |
| author_facet | Lopes, Pedro T. P. Roidos, Nikolaos |
| contents | We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data, we show that the solution exists in the maximal $L^q$-regularity space for all times and becomes instantaneously smooth in space and time, where the maximal $L^q$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we provide precise information concerning the asymptotic behavior of the solution close to the conical tips in terms of the local geometry. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1903_06628 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities Lopes, Pedro T. P. Roidos, Nikolaos Analysis of PDEs 35K58, 35K65, 35K90, 35K91, 35R01 We consider the Cahn-Hilliard equation on manifolds with conical singularities. For appropriate initial data, we show that the solution exists in the maximal $L^q$-regularity space for all times and becomes instantaneously smooth in space and time, where the maximal $L^q$-regularity is obtained in the sense of Mellin-Sobolev spaces. Moreover, we provide precise information concerning the asymptotic behavior of the solution close to the conical tips in terms of the local geometry. |
| title | Smoothness and long time existence for solutions of the Cahn-Hilliard equation on manifolds with conical singularities |
| topic | Analysis of PDEs 35K58, 35K65, 35K90, 35K91, 35R01 |
| url | https://arxiv.org/abs/1903.06628 |