Decay estimate for subcritical semilinear damped wave equations with slowly decreasing data
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913738180788224 |
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| author | Fujiwara, Kazumasa Georgiev, Vladimir |
| author_facet | Fujiwara, Kazumasa Georgiev, Vladimir |
| contents | We study the decay properties of non-negative solutions to the one-dimensional defocusing damped wave equation in the Fujita subcritical case under a specific initial condition. Specifically, we assume that the initial data are positive, satisfy a condition ensuring the positiveness of solutions, and exhibit polynomial decay at infinity.
To show the decay properties of the solution, we construct suitable supersolutions composed of an explicit function satisfying an ordinary differential inequality and the solution of the linear damped wave equation. Our estimates correspond to the optimal ones inferred from the analysis of the heat equation. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2503_12140 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decay estimate for subcritical semilinear damped wave equations with slowly decreasing data Fujiwara, Kazumasa Georgiev, Vladimir Analysis of PDEs 35B40, 35B33, 35B51 We study the decay properties of non-negative solutions to the one-dimensional defocusing damped wave equation in the Fujita subcritical case under a specific initial condition. Specifically, we assume that the initial data are positive, satisfy a condition ensuring the positiveness of solutions, and exhibit polynomial decay at infinity. To show the decay properties of the solution, we construct suitable supersolutions composed of an explicit function satisfying an ordinary differential inequality and the solution of the linear damped wave equation. Our estimates correspond to the optimal ones inferred from the analysis of the heat equation. |
| title | Decay estimate for subcritical semilinear damped wave equations with slowly decreasing data |
| topic | Analysis of PDEs 35B40, 35B33, 35B51 |
| url | https://arxiv.org/abs/2503.12140 |