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arXiv · 2404.12058

Nonexistence of solutions to parabolic problems with a potential on weighted graphs

Dario D. Monticelli·Fabio Punzo·Jacopo Somaglia
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Abstract

We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper bound on the Laplacian of the distance and a suitable weighted space-time volume growth condition, we show that no global solutions exists. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type.

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Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia. 2024-04-18. Nonexistence of solutions to parabolic problems with a potential on weighted graphs. https://arxiv.org/abs/2404.12058

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