Existence of solutions to the semilinear damped wave equation with non-$L^2$ slowly decaying data : polynomial nonlinearity case
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917451613077504 |
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| author | Ikeda, Masahiro Inui, Takahisa Wakasugi, Yuta |
| author_facet | Ikeda, Masahiro Inui, Takahisa Wakasugi, Yuta |
| contents | We study the Cauchy problem of the semilinear damped wave equation with polynomial nonlinearity, and establish the local and global existence of the solution for slowly decaying initial data not belonging to $L^2(\mathbb{R}^n)$ in general. Our approach is based on the $L^p$-$L^q$ estimates of linear solutions and the fractional Leibniz rule in suitable homogeneous Besov spaces. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_10768 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Existence of solutions to the semilinear damped wave equation with non-$L^2$ slowly decaying data : polynomial nonlinearity case Ikeda, Masahiro Inui, Takahisa Wakasugi, Yuta Analysis of PDEs 35L71, 35A01 We study the Cauchy problem of the semilinear damped wave equation with polynomial nonlinearity, and establish the local and global existence of the solution for slowly decaying initial data not belonging to $L^2(\mathbb{R}^n)$ in general. Our approach is based on the $L^p$-$L^q$ estimates of linear solutions and the fractional Leibniz rule in suitable homogeneous Besov spaces. |
| title | Existence of solutions to the semilinear damped wave equation with non-$L^2$ slowly decaying data : polynomial nonlinearity case |
| topic | Analysis of PDEs 35L71, 35A01 |
| url | https://arxiv.org/abs/2505.10768 |