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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 …
math.AP2024
The porous medium equation on noncompact manifolds with nonnegative Ricci curvature: a Green function approach
Gabriele Grillo, Dario D. Monticelli, Fabio Punzo
We consider the porous medium equation (PME) on complete noncompact manifolds of nonnegative Ricci curvature. We require nonparabolicity of the manifold and construct a natural…