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math.AP2024
On the uniqueness for the heat equation with density on infinite graphs
Giulia Meglioli
We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bound…
math.AP2024
Blow-up and global existence for semilinear parabolic equations on infinite graphs
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
We investigate existence of global in time solutions and blow-up of solutions to the semilinear heat equation posed on infinite graphs. The source term is a general function …