Nonexistence of solutions to parabolic problems with a potential on weighted graphs
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.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2024
- DOI:
- 10.48550/arXiv.2404.12058
- arXiv:
- arXiv:2404.12058
- Bibcode:
- 2024arXiv240412058M
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35A01;
- 35A02;
- 35B44;
- 35K05;
- 35K58;
- 35R02
- E-Print:
- Fixed minor typos