Blow-up of solutions to semilinear wave equations with spatial derivatives
Fuente:
arXiv
Guardado en:
| Autores principales: | , , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2024
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866916273751851008 |
|---|---|
| author | Shao, Kerun Takamura, Hiroyuki Wang, Chengbo |
| author_facet | Shao, Kerun Takamura, Hiroyuki Wang, Chengbo |
| contents | For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obtained for both critical cases and subcritical cases, for all spatial dimensions $n>1$. It is achieved uniformly by constructing the integral equations, deriving the ordinary differential inequality system, and iteration argument. Combined with the former works, the sharp lifespan estimates for this problem are completely established, at least for the spherical symmetric case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_02098 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Blow-up of solutions to semilinear wave equations with spatial derivatives Shao, Kerun Takamura, Hiroyuki Wang, Chengbo Analysis of PDEs 35L05, 35L71, 35B30, 35B33, 35B44 For small-amplitude semilinear wave equations with power type nonlinearity on the first-order spatial derivative, the expected sharp upper bound on the lifespan of solutions is obtained for both critical cases and subcritical cases, for all spatial dimensions $n>1$. It is achieved uniformly by constructing the integral equations, deriving the ordinary differential inequality system, and iteration argument. Combined with the former works, the sharp lifespan estimates for this problem are completely established, at least for the spherical symmetric case. |
| title | Blow-up of solutions to semilinear wave equations with spatial derivatives |
| topic | Analysis of PDEs 35L05, 35L71, 35B30, 35B33, 35B44 |
| url | https://arxiv.org/abs/2406.02098 |