Singular convergence for semilinear wave equations with steep potential well
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912913021730816 |
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| author | Prizzi, Martino |
| author_facet | Prizzi, Martino |
| contents | We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom of the well, with Dirichlet condition on the boundary. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17279 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Singular convergence for semilinear wave equations with steep potential well Prizzi, Martino Analysis of PDEs 35L10, 35B25 We consider a semilinear wave equation in the whole space with a deep potential well. We prove that as the depth of the well tends to infinity, the solutions of the equation converge to the solutions of a wave equation defined on the bottom of the well, with Dirichlet condition on the boundary. |
| title | Singular convergence for semilinear wave equations with steep potential well |
| topic | Analysis of PDEs 35L10, 35B25 |
| url | https://arxiv.org/abs/2602.17279 |