Work

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

Year: 2025

Type: article

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.

Source: Journal of Differential Equations

DOI: 10.1016/j.jde.2025.113782

Authors: Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia

Institution: Politecnico di Milano

Language: English

Topic: Nonlinear Partial Differential Equations

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: European Commission, Ministero dell'Università e della Ricerca, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni