Blow-up results for a Nakao-type problem with a time-dependent damping term and derivative-type nonlinearities
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2025
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866914105158270976 |
|---|---|
| author | Li, Yuequn Palmieri, Alessandro |
| author_facet | Li, Yuequn Palmieri, Alessandro |
| contents | In this paper, we consider a semilinear system of damped wave equations coupled through power nonlinearities of derivative-type. In particular, we consider a classical damped wave equation, i.e., with constant coefficients, and a wave equation with a time-dependent coefficient for the damping term. For this time-dependent coefficient we analyze two cases: the scale-invariant case and the scattering producing case. We prove blow-up results and derive upper bound estimates for the lifespan of local solutions. Our approach is based on an iteration argument for a couple of functionals related to the components of a local solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18378 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Blow-up results for a Nakao-type problem with a time-dependent damping term and derivative-type nonlinearities Li, Yuequn Palmieri, Alessandro Analysis of PDEs 35B44, 35G55, 35L52, 35L71 In this paper, we consider a semilinear system of damped wave equations coupled through power nonlinearities of derivative-type. In particular, we consider a classical damped wave equation, i.e., with constant coefficients, and a wave equation with a time-dependent coefficient for the damping term. For this time-dependent coefficient we analyze two cases: the scale-invariant case and the scattering producing case. We prove blow-up results and derive upper bound estimates for the lifespan of local solutions. Our approach is based on an iteration argument for a couple of functionals related to the components of a local solution. |
| title | Blow-up results for a Nakao-type problem with a time-dependent damping term and derivative-type nonlinearities |
| topic | Analysis of PDEs 35B44, 35G55, 35L52, 35L71 |
| url | https://arxiv.org/abs/2510.18378 |