Solvability of a semilinear heat equation on Riemannian manifolds

Autor:	Takahashi, Jin, Yamamoto, Hikaru
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs Mathematics - Differential Geometry
Druh dokumentu:	Working Paper
Popis:	We study the solvability of the initial value problem for the semilinear heat equation $u_t-\Delta u=u^p$ in a Riemannian manifold $M$ with a nonnegative Radon measure $\mu$ on $M$ as initial data. We give sharp conditions on the local-in-time solvability of the problem for complete and connected $M$ with positive injectivity radius and bounded sectional curvature. Comment: 46 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2207.03731 Zobrazit plný text záznamu View this record from Arxiv