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Nonexistence Results for a General Class of Parabolic Problems with a Potential on Weighted Graphs

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arxiv 2504.03878 v1 pith:4SPRFDEC submitted 2025-04-04 math.AP

Dorothea-Enrica von Criegern This is my paper · ORCID
classification math.AP
keywords nonexistencepotentialclassconditionsequationfunctiongraphsparabolic
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We establish nonexistence conditions for nonnegative nontrivial solutions to a class of semilinear parabolic equations with a positive potential on weighted graphs, extending results in arXiv:2404.12058 [math.AP] to a broader setting that includes both the Porous Medium Equation and the Fast Diffusion Equation. We identify conditions related to the graph's geometry, the potential's behaviour at infinity, and bounds on the Laplacian of the distance function under which nonexistence holds. Using a test function argument, we derive explicit parameter ranges for nonexistence.

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Cited by 1 Pith paper

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  1. Nonexistence results for the semilinear wave equation on graphs

    math.AP 2025-06 reject novelty 6.0 of 10

    On infinite weighted graphs, if the graph Laplacian of the distance grows slowly and suitable weighted volume growth holds, every very weak solution of the semilinear wave inequality is identically zero.

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