An optimal Liouville theorem for the porous medium equation

Autor:	Araújo, Damião J., Teymurazyan, Rafayel
Rok vydání:	2022
Předmět:	Mathematics - Analysis of PDEs 35B53 35K55 35K65 76S05
Druh dokumentu:	Working Paper
Popis:	Under a sharp asymptotic growth condition at infinity, we prove a Liouville type theorem for the inhomogeneous porous medium equation, provided it stays universally close to the heat equation. Additionally, for the homogeneous equation, we show that for the conclusion to hold, it is enough to assume the sharp asymptotic growth at infinity only in the space variable. The results are optimal, meaning that the growth condition at infinity cannot be weakened. Comment: 7 pages
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2201.02031 Zobrazit plný text záznamu View this record from Arxiv