5 papers
Fractional porous medium equation on manifolds with nonnegative Ricci curvature: existence of solutions and smoothing effects via potential methods
Dorothea-Enrica von Criegern, Gabriele Grillo, Dario Daniele Monticelli
We study the fractional porous medium equation on complete noncompact Riemannian manifolds with nonnegative Ricci curvature for and . Assuming that the manifold i…
A porous medium equation with rough weights: sharp Widder theory
Gabriele Grillo, Matteo Muratori, Troy Petitt +1
We establish an optimal \emph{Widder theory} for a weighted porous medium equation with rough and inhomogeneous density that may be singular at a point and tends to zero at spatial…
Nonexistence of Solutions to classes of parabolic inequalities in the Riemannian setting
Dorothea-Enrica von Criegern, Gabriele Grillo, Dario Monticelli
We establish conditions for nonexistence of global solutions for a class of quasilinear parabolic problems with a potential on complete, non-compact Riemannian manifolds, including…
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 …
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…