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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2210.04603 |
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| _version_ | 1866910846583570432 |
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| author | Antonelli, Paolo Cannarsa, Piermarco Shakarov, Boris |
| author_facet | Antonelli, Paolo Cannarsa, Piermarco Shakarov, Boris |
| contents | We consider a nonlinear parabolic equation with a nonlocal term, which preserves the $L^2$-norm of the solution. We study the local and global well posedness on a bounded domain, as well as the whole Euclidean space, in $H^1$. Then we study the asymptotic behavior of solutions. In general, we obtain weak convergence in H^1 to a stationary state. For a ball, we prove strong asymptotic convergence to the ground state when the initial condition is positive. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_04603 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Existence and asymptotic behavior for $L^2$-norm preserving nonlinear heat equations Antonelli, Paolo Cannarsa, Piermarco Shakarov, Boris Analysis of PDEs 35K55, 35B40 We consider a nonlinear parabolic equation with a nonlocal term, which preserves the $L^2$-norm of the solution. We study the local and global well posedness on a bounded domain, as well as the whole Euclidean space, in $H^1$. Then we study the asymptotic behavior of solutions. In general, we obtain weak convergence in H^1 to a stationary state. For a ball, we prove strong asymptotic convergence to the ground state when the initial condition is positive. |
| title | Existence and asymptotic behavior for $L^2$-norm preserving nonlinear heat equations |
| topic | Analysis of PDEs 35K55, 35B40 |
| url | https://arxiv.org/abs/2210.04603 |