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 exist. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type.
Nonexistence of solutions to parabolic problems with a potential on weighted graphs
Monticelli, Dario D.;Punzo, Fabio;Somaglia, Jacopo
2026-01-01
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 exist. We also discuss the optimality of the hypotheses, thus recovering a critical exponent phenomenon of Fujita type.File in questo prodotto:
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Monticelli, Punzo, Somaglia - Nonexistence of solutions to parabolic problems with a potential on weghted graphs.pdf
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