76 citations · 172 across the 24 of their papers we have counts for
7 papers · 1 filter
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…
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…
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…
The generalized porous medium equation on graphs: existence and uniqueness of solutions with data
Davide Bianchi, Alberto G. Setti, Radoslaw K. Wojciechowski
We study solutions of the generalized porous medium equation on infinite graphs. For nonnegative or nonpositive integrable data, we prove the existence and uniqueness of mild solut…
Qualitative properties of bounded subsolutions of nonlinear PDEs
Davide Bianchi, Stefano Pigola, Alberto G. Setti
We study decay and compact support properties of positive and bounded solutions of on the exterior of a compact set of a complete manifold with rotationally sym…
The shifted wave equation on Damek--Ricci spaces and on homogeneous trees
Jean-Philippe Anker, Pierre Martinot, Emmanuel Pedon +1
We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' pri…