Global existence of solutions for semilinear damped wave equation with nonlinearities of derivative type
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866917131776425984 |
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| author | Van Duong, Dinh Dao, Tuan Anh |
| author_facet | Van Duong, Dinh Dao, Tuan Anh |
| contents | In this paper, we consider the semilinear damped wave equation with nonlinearities of derivative type $|u_t|^p$. We observe that this problem admits a unique global (in time) solution with small initial data for all $p > 1$ in low spatial dimensions $n=1,2$. This result provides new insights into semilinear damped wave equations and complements the existing literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_06789 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global existence of solutions for semilinear damped wave equation with nonlinearities of derivative type Van Duong, Dinh Dao, Tuan Anh Analysis of PDEs 35A01, 35B33, 35L15, 35L71 In this paper, we consider the semilinear damped wave equation with nonlinearities of derivative type $|u_t|^p$. We observe that this problem admits a unique global (in time) solution with small initial data for all $p > 1$ in low spatial dimensions $n=1,2$. This result provides new insights into semilinear damped wave equations and complements the existing literature. |
| title | Global existence of solutions for semilinear damped wave equation with nonlinearities of derivative type |
| topic | Analysis of PDEs 35A01, 35B33, 35L15, 35L71 |
| url | https://arxiv.org/abs/2512.06789 |