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math.AP2026
The generalized porous medium equation on graphs: well-posedness, extinction, and mass conservation
Davide Bianchi, Bobo Hua, Alberto G. Setti +1
We study the Cauchy problem for the generalized porous medium equation on infinite weighted graphs. For a general nonlinearity, we establish Dirichlet comparison and weak maximum p…
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.AP2026
Proper solutions of the -flow and the Green kernel of the -Laplacian
Luca Benatti, Luciano Mari, Marco Rigoli +2
We show existence and optimal growth estimate for the weak inverse mean curvature flow issuing from a point, on manifolds with certain curvature and isoperimetric conditions. These…