Uniform estimates for solutions of nonlinear focusing damped wave equations
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914709401239552 |
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| author | Perrin, Thomas |
| author_facet | Perrin, Thomas |
| contents | For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result applies in particular to the case of a cubic equation on a bounded domain of dimension 3. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_06541 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Uniform estimates for solutions of nonlinear focusing damped wave equations Perrin, Thomas Analysis of PDEs For a damped wave (or Klein-Gordon) equation on a bounded domain, with a focusing power-like nonlinearity satisfying some growth conditions, we prove that a global solution is bounded in the energy space, uniformly in time. Our result applies in particular to the case of a cubic equation on a bounded domain of dimension 3. |
| title | Uniform estimates for solutions of nonlinear focusing damped wave equations |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2403.06541 |