6 citations · 19 across the 55 of their papers we have counts for
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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…
Uniqueness for degenerate parabolic equations in weighted spaces
Camilla Nobili, Fabio Punzo
We study uniqueness of solutions to degenerate parabolic problems, posed in bounded domains, where no boundary conditions are imposed. Under suitable assumptions on the operator, u…
Blow-up and global existence for the inhomogeneous porous medium equation with reaction
Giulia Meglioli, Fabio Punzo
We study finite time blow-up and global existence of solutions to the Cauchy problem for the porous medium equation with a variable density and a power-like reaction term. W…
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…