An optimal Liouville theorem for the porous medium equation
Analysis of PDEs
2022-01-07 v1
Abstract
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.
Cite
@article{arxiv.2201.02031,
title = {An optimal Liouville theorem for the porous medium equation},
author = {Damião J. Araújo and Rafayel Teymurazyan},
journal= {arXiv preprint arXiv:2201.02031},
year = {2022}
}
Comments
7 pages