Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912149275672576 |
|---|---|
| author | Hisa, Kotaro Ishige, Kazuhiro |
| author_facet | Hisa, Kotaro Ishige, Kazuhiro |
| contents | We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy--Dirichlet problem, we obtain sharp necessary conditions and sufficient conditions on the existence of nonnegative solutions and identify optimal singularities of solvable nonnegative initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_06200 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition Hisa, Kotaro Ishige, Kazuhiro Analysis of PDEs 35A01, 35A21, 35K20 We study qualitative properties of initial traces of nonnegative solutions to a semilinear heat equation in a smooth domain under the Dirichlet boundary condition. Furthermore, for the corresponding Cauchy--Dirichlet problem, we obtain sharp necessary conditions and sufficient conditions on the existence of nonnegative solutions and identify optimal singularities of solvable nonnegative initial data. |
| title | Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition |
| topic | Analysis of PDEs 35A01, 35A21, 35K20 |
| url | https://arxiv.org/abs/2412.06200 |