Nonexistence results for a general class of parabolic problems with a potential on weighted graphs
Abstract
Abstract We establish nonexistence conditions for nonnegative nontrivial solutions to a class of semilinear parabolic equations with a positive potential on weighted graphs, extending the results of Monticelli, Punzo, and Somaglia (2024) to a broader setting. Our framework includes both the Porous Medium Equation and the Fast Diffusion Equation. We identify conditions related to the graph’s geometry, the potential’s behaviour at infinity, and bounds on the Laplacian of the distance function under which nonexistence holds. Using a test function argument, we derive explicit parameter ranges for nonexistence.
Fields of Study & Subjects
Nonlinear Partial Differential Equations
Geometric Analysis and Curvature Flows
Contact Mechanics and Variational Inequalities
Publication details
- Journal / source
- Nonlinear Differential Equations and Applications NoDEA
- Publisher
- Springer Science and Business Media LLC
- Volume
- 33
- Issue
- 2
- Publication date
- 10 January 2026
- Language
- EN