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math.AP2026
The fractional Porous Medium Equation on graphs
Elvise Berchio, Federico Santagati, Maria Vallarino
We study the fractional porous medium equation on connected infinite graphs with no local finiteness assumption. We introduce a notion of weak dual solution adapted to the discrete…
math.AP2026
Semilinear Diffusion Equations on Infinite Graphs: The Dissipative and Lipschitz Cases
Elvise Berchio, Davide Bianchi, Alberto G. Setti +1
We study a class of semilinear diffusion equations on infinite, connected, weighted graphs, focusing on two types of nonlinearities: monotone decreasing and Lipschitz continuous. U…
math.AP2025
Smoothing effects and extinction in finite time for fractional fast diffusions on Riemannian manifolds
Elvise Berchio, Matteo Bonforte, Gabriele Grillo
We study nonnegative solutions to the Cauchy problem for the Fractional Fast Diffusion Equation on a suitable class of connected, noncompact Riemannian manifolds. This parabolic eq…