135 citations · 360 across the 30 of their papers we have counts for
4 papers · 1 filter
Global existence of solutions and smoothing effects for classes of reaction-diffusion equations on manifolds
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
We consider the porous medium equation with a power-like reaction term, posed on Riemannian manifolds. Under certain assumptions on and in (1.1), and for small enough nonne…
Smoothing effects and infinite time blowup for reaction-diffusion equations: an approach via Sobolev and Poincaré inequalities
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
We consider reaction-diffusion equations either posed on Riemannian manifolds or in the Euclidean weighted setting, with pow\-er-type nonlinearity and slow diffusion of porous medi…
Fast diffusion on noncompact manifolds: well-posedness theory and connections with semilinear elliptic equations
Gabriele Grillo, Matteo Muratori, Fabio Punzo
We investigate the well-posedness of the fast diffusion equation (FDE) in a wide class of noncompact Riemannian manifolds. Existence and uniqueness of solutions for globally integr…
The Fractional Porous Medium Equation on the hyperbolic space
Elvise Berchio, Matteo Bonforte, Debdip Ganguly +1
We consider the nonlinear degenerate parabolic equation of porous medium type, whose diffusion is driven by the (spectral) fractional Laplacian on the hyperbolic space. We provide…