Effect of additional regularity for the initial data on semi-linear $σ$-evolution equations with different damping types
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866912230427066368 |
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| author | Van Duong, Dinh Dao, Tuan Anh |
| author_facet | Van Duong, Dinh Dao, Tuan Anh |
| contents | In this paper, we would like to study the critical exponent for semi-linear $σ$-evolution equations with different damping types under the influence of additional regularity for the initial data. On the one hand, we establish the existence of global (in time) solutions for small initial data and the blow-up in finite time solutions in the supercritical case and the subcritical case, respectively. The very interesting phenomenon is that the critical case belonging to the global solution range or the blow-up solution range depends heavily on the assumption of additional regularity for the initial data. Furthermore, we are going to provide lifespan estimates for solutions when the blow-up phenomenon occurs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_08183 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Effect of additional regularity for the initial data on semi-linear $σ$-evolution equations with different damping types Van Duong, Dinh Dao, Tuan Anh Analysis of PDEs 35A01, 35B33, 35L71 In this paper, we would like to study the critical exponent for semi-linear $σ$-evolution equations with different damping types under the influence of additional regularity for the initial data. On the one hand, we establish the existence of global (in time) solutions for small initial data and the blow-up in finite time solutions in the supercritical case and the subcritical case, respectively. The very interesting phenomenon is that the critical case belonging to the global solution range or the blow-up solution range depends heavily on the assumption of additional regularity for the initial data. Furthermore, we are going to provide lifespan estimates for solutions when the blow-up phenomenon occurs. |
| title | Effect of additional regularity for the initial data on semi-linear $σ$-evolution equations with different damping types |
| topic | Analysis of PDEs 35A01, 35B33, 35L71 |
| url | https://arxiv.org/abs/2502.08183 |