Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915037560438784 |
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| author | Shakarov, Boris |
| author_facet | Shakarov, Boris |
| contents | We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy space. Then, we consider the solutions' asymptotic behavior. We prove strong convergence to a stationary state and asymptotic convergence to the ground state in bounded domains when the initial condition is positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_18532 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow Shakarov, Boris Analysis of PDEs 35K55, 35B40 We consider a nonlinear parabolic model that forces solutions to stay on a $L^2$-sphere through a nonlocal term in the equation. We study the local and global well-posedness on a bounded domain and the whole Euclidean space in the energy space. Then, we consider the solutions' asymptotic behavior. We prove strong convergence to a stationary state and asymptotic convergence to the ground state in bounded domains when the initial condition is positive. |
| title | Global solutions and Asymptotic Behavior to a Norm-preserving Non-local Parabolic Flow |
| topic | Analysis of PDEs 35K55, 35B40 |
| url | https://arxiv.org/abs/2411.18532 |