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arXiv:2112.01733 [math.AP]AbstractReferencesReviewsResources

The generalized porous medium equation on graphs: existence and uniqueness of solutions with $\ell^1$ data

Davide Bianchi, Alberto G. Setti, Radoslaw K. Wojciechowski

Published 2021-12-03, updated 2022-03-30Version 2

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.

Categories: math.AP, math.CO
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