Nonexistence of solutions to parabolic problems with a potential on weighted graphs
Analysis of PDEs
2025-03-10 v3
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.
Cite
@article{arxiv.2404.12058,
title = {Nonexistence of solutions to parabolic problems with a potential on weighted graphs},
author = {Dario D. Monticelli and Fabio Punzo and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2404.12058},
year = {2025}
}
Comments
Fixed minor typos