135 citations · 360 across the 30 of their papers we have counts for
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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…
A general nonlinear characterization of stochastic incompleteness
Gabriele Grillo, Kazuhiro Ishige, Matteo Muratori +1
Stochastic incompleteness of a Riemannian manifold amounts to the nonconservation of probability for the heat semigroup on . We show that this property is equivalent to the…
Global existence for reaction-diffusion evolution equations driven by the -Laplacian on manifolds
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
We consider reaction-diffusion equations driven by the -Laplacian on noncompact, infinite volume manifolds assumed to support the Sobolev inequality and, in some cases, to have…
The porous medium equation with large data on Cartan-Hadamard manifolds under general curvature bounds
Gabriele Grillo, Matteo Muratori, Fabio Punzo
We consider very weak solutions of the Cauchy problem for the porous medium equation on Cartan-Hadamard manifolds, that are assumed to satisfy general curvature bounds and to be st…
Blow-up versus global existence of solutions for reaction-diffusion equations on classes of Riemannian manifolds
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
It is well known from the work of [2] that the Fujita phenomenon for reaction-diffusion evolution equations with power nonlinearities does not occur on the hyperbolic space $\mathb…
The Fractional Porous Medium Equation on noncompact Riemannian manifolds
Elvise Berchio, Matteo Bonforte, Gabriele Grillo +1
We study nonnegative solutions to the Fractional Porous Medium Equation on a suitable class of connected, noncompact Riemannian manifolds. We provide existence and smoothing estima…