Quasilinear parabolic equations with superlinear nonlinearities in critical spaces
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_ | 1866917872096247808 |
|---|---|
| author | Matioc, Bogdan-Vasile Roberti, Luigi Walker, Christoph |
| author_facet | Matioc, Bogdan-Vasile Roberti, Luigi Walker, Christoph |
| contents | Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations $u'=A(u)u+f(u)$ is established in a certain critical case of strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ for the domains of the (superlinear) function $u\mapsto f(u)$ and the quasilinear part $u\mapsto A(u)$. Based upon regularizing effects of parabolic equations, it is proven that the solution map generates a semiflow in a critical intermediate space. The applicability of the abstract results is demonstrated by several examples including a model for atmospheric flows and semilinear and quasilinear evolution equations with scaling invariance for which well-posedness in the critical scaling invariant intermediate spaces is shown. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_05067 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quasilinear parabolic equations with superlinear nonlinearities in critical spaces Matioc, Bogdan-Vasile Roberti, Luigi Walker, Christoph Analysis of PDEs Well-posedness in time-weighted spaces for quasilinear (and semilinear) parabolic evolution equations $u'=A(u)u+f(u)$ is established in a certain critical case of strict inclusion $\mathrm{dom}(f)\subsetneq \mathrm{dom}(A)$ for the domains of the (superlinear) function $u\mapsto f(u)$ and the quasilinear part $u\mapsto A(u)$. Based upon regularizing effects of parabolic equations, it is proven that the solution map generates a semiflow in a critical intermediate space. The applicability of the abstract results is demonstrated by several examples including a model for atmospheric flows and semilinear and quasilinear evolution equations with scaling invariance for which well-posedness in the critical scaling invariant intermediate spaces is shown. |
| title | Quasilinear parabolic equations with superlinear nonlinearities in critical spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.05067 |