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math.AP2020
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…
math.AP2020★ 2 cited
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…
math.AP2020
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…