The generalized porous medium equation on graphs: existence and uniqueness of solutions with $\ell^1$ data
Analysis of PDEs
2022-03-31 v2 Combinatorics
Abstract
We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solutions on any graph. For changing sign integrable data, we show existence and uniqueness under extra assumptions such as local finiteness or a uniform lower bound on the node measure.
Keywords
Cite
@article{arxiv.2112.01733,
title = {The generalized porous medium equation on graphs: existence and uniqueness of solutions with $\ell^1$ data},
author = {Davide Bianchi and Alberto G. Setti and Radoslaw K. Wojciechowski},
journal= {arXiv preprint arXiv:2112.01733},
year = {2022}
}