Center stable manifolds for the radial semi-linear wave equation outside a ball
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911763040043008 |
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| author | Duyckaerts, Thomas Yang, Jianwei Urban |
| author_facet | Duyckaerts, Thomas Yang, Jianwei Urban |
| contents | We consider the nonlinear wave equation, with a large exponent, power-like non-linearity, outside a ball of the Euclidean 3-dimensional space. In a previous article, we have proved that any global solution converges, up to a radiation term, to a stationary solution of the equation. In this work, we construct the center-stable manifold associated to each of the stationary solution, giving a complete description of the dynamics of global solutions. We also study the behavior of solutions close to each of the center-stable manifold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12581 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Center stable manifolds for the radial semi-linear wave equation outside a ball Duyckaerts, Thomas Yang, Jianwei Urban Analysis of PDEs 35L05, 35A01, 35B40, 35B44, 37K40 We consider the nonlinear wave equation, with a large exponent, power-like non-linearity, outside a ball of the Euclidean 3-dimensional space. In a previous article, we have proved that any global solution converges, up to a radiation term, to a stationary solution of the equation. In this work, we construct the center-stable manifold associated to each of the stationary solution, giving a complete description of the dynamics of global solutions. We also study the behavior of solutions close to each of the center-stable manifold. |
| title | Center stable manifolds for the radial semi-linear wave equation outside a ball |
| topic | Analysis of PDEs 35L05, 35A01, 35B40, 35B44, 37K40 |
| url | https://arxiv.org/abs/2401.12581 |