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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2411.17512 |
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| _version_ | 1866929605888180224 |
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| author | Apushkinskaya, Darya Tikhomirov, Sergey Uraltseva, Nina |
| author_facet | Apushkinskaya, Darya Tikhomirov, Sergey Uraltseva, Nina |
| contents | We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial data from the space $W^{2-2/q}_q$ with $q > 3$, there exists a solution in the space $W^{2,1}_q$, where the interface boundary exhibits Holder continuity with an exponent $1/2$. Furthermore for initial data from the space $W^2_\infty$, it is proven that the interface boundary satisfies the Lipschitz condition. It is shown that for non-transversal initial data, solutions with an interface boundary do not exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_17512 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Properties of the phase boundary in the parabolic problem with hysteresis Apushkinskaya, Darya Tikhomirov, Sergey Uraltseva, Nina Analysis of PDEs 35K15, 35R35, 47J40 We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial data from the space $W^{2-2/q}_q$ with $q > 3$, there exists a solution in the space $W^{2,1}_q$, where the interface boundary exhibits Holder continuity with an exponent $1/2$. Furthermore for initial data from the space $W^2_\infty$, it is proven that the interface boundary satisfies the Lipschitz condition. It is shown that for non-transversal initial data, solutions with an interface boundary do not exist. |
| title | Properties of the phase boundary in the parabolic problem with hysteresis |
| topic | Analysis of PDEs 35K15, 35R35, 47J40 |
| url | https://arxiv.org/abs/2411.17512 |