Initial traces of solutions to a semilinear heat equation under the Dirichlet boundary condition

Autor:	Hisa, Kotaro, Ishige, Kazuhiro
Rok vydání:	2024
Předmět:	Mathematics - Analysis of PDEs 35A01 35A21 35K20
Druh dokumentu:	Working Paper
Popis:	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. Comment: 46pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2412.06200 Zobrazit plný text záznamu View this record from Arxiv