On semilinear damped wave equations with initial data in homogeneous Sobolev spaces
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917426367561728 |
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| author | Matsunaga, Mitsuhiro |
| author_facet | Matsunaga, Mitsuhiro |
| contents | In this paper, we study semilinear damped equations $u_{tt}+u_t-Δu=|u|^p$ with the initial data in $({\dot{H}^{-γ}}\cap H^s)\times({\dot{H}^{-γ}}\cap L^2)$. Chen-Reissig (2023) studied the case $0<γ<\frac{n}{2}$ and showed that the exponent $p_{\mathrm{crit}}=1+\frac{4}{n+2γ}$ of $p$ distinguishes the time global existence and the blow-up of solution. In this paper, we discuss the case $γ\ge\frac{n}{2}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_05670 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On semilinear damped wave equations with initial data in homogeneous Sobolev spaces Matsunaga, Mitsuhiro Analysis of PDEs In this paper, we study semilinear damped equations $u_{tt}+u_t-Δu=|u|^p$ with the initial data in $({\dot{H}^{-γ}}\cap H^s)\times({\dot{H}^{-γ}}\cap L^2)$. Chen-Reissig (2023) studied the case $0<γ<\frac{n}{2}$ and showed that the exponent $p_{\mathrm{crit}}=1+\frac{4}{n+2γ}$ of $p$ distinguishes the time global existence and the blow-up of solution. In this paper, we discuss the case $γ\ge\frac{n}{2}$. |
| title | On semilinear damped wave equations with initial data in homogeneous Sobolev spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2511.05670 |