Nonexistence of solutions to parabolic problems with a potential on weighted graphs
| Autor: | Monticelli, Dario D., Punzo, Fabio, Somaglia, Jacopo |
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| Rok vydání: | 2024 |
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| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: Fixed minor typos |
| Databáze: | arXiv |
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