2 citations · 4 across the 18 of their papers we have counts for
20 papers
Semigroup Criteria for Blow-up and Global Existence of Semilinear Heat Equations on Metric Measure Spaces
Giulia Meglioli, Fabio Punzo
We study finite-time blow-up and global existence for semilinear heat equations with time-dependent reaction coefficients on metric measure spaces. For convex nonlinearities, we es…
Global existence for a Leibenson type equation with reaction on Riemannian manifolds
Giulia Meglioli, Francescantonio Oliva, Francesco Petitta
We show a global existence result for a doubly nonlinear porous medium type equation of the form on a complete and non-compact Riemannian manifold of…
Phragmèn-Lindelöf type theorems for parabolic equations on infinite graphs
Stefano Biagi, Giulia Meglioli, Fabio Punzo
We obtain the Phragmèn-Lindelöf principle on combinatorial infinite weighted graphs for the Cauchy problem associated to a certain class of parabolic equations with a variable dens…
Uniqueness of solutions to elliptic and parabolic equations on metric graphs
Giulia Meglioli, Fabio Punzo
We investigate uniqueness of solutions to certain classes of elliptic and parabolic equations posed on metric graphs. In particular, we address the linear Schrödinger equation with…
On the uniqueness for the heat equation with density on infinite graphs
Giulia Meglioli
We study the uniqueness of solutions to a class of heat equations with positive density posed on infinite weighted graphs. We separately consider the case when the density is bound…
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 …
Uniqueness for local-nonlocal elliptic equations
Stefano Biagi, Giulia Meglioli, Fabio Punzo
We study mixed local and nonlocal elliptic equation with a variable coefficient . Under suitable assumptions on the behaviour at infinity of , we obtain uniqueness of solutio…
A Liouville theorem for elliptic equations with a potential on infinite graphs
Stefano Biagi, Giulia Meglioli, Fabio Punzo
We investigate the validity of the Liouville property for a class of elliptic equations with a potential, posed on infinite graphs. Under suitable assumptions on the graph and on t…
Uniqueness in weighted spaces for the Schrödinger equation on infinite graphs
Giulia Meglioli, Fabio Punzo
We investigate uniqueness of solutions to Schrödinger-type elliptic equations posed on infinite graphs. Solutions are assumed to belong to suitable weighted spaces where $…
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…
Uniqueness in weighted Lebesgue spaces for an elliptic equation with drift on manifolds
Giulia Meglioli, Alberto Roncoroni
We investigate the uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of elliptic equations with a drift posed on a complete, noncompact, Riemannian manifold…
Uniqueness for fractional parabolic and elliptic equations with drift
Giulia Meglioli, Fabio Punzo
We investigate uniqueness, in suitable weighted Lebesgue spaces, of solutions to a class of fractional parabolic and elliptic equations with a drift.
Global existence and blow-up of solutions to the porous medium equation with reaction and singular coefficients
Giulia Meglioli
We study global in time existence versus blow-up in finite time of solutions to the Cauchy problem for the porous medium equation with a variable density and a power-like re…
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…
Nonexistence of solutions to quasilinear parabolic equations with a potential in bounded domains
Giulia Meglioli, Dario D. Monticelli, Fabio Punzo
We are concerned with nonexistence results for a class of quasilinear parabolic differential problems with a potential in , where is a bounded domain. In pa…
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…
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…
Blow-up and global existence for solutions to the porous medium equation with reaction and fast decaying density
Giulia Meglioli, Fabio Punzo
We are concerned with nonnegative solutions to the Cauchy problem for the porous medium equation with a variable density and a power-like reaction term with . The…
Blow-up and global existence for solutions to the porous medium equation with reaction and slowly decaying density
Giulia Meglioli, Fabio Punzo
We study existence of global solutions and finite time blow-up of solutions to the Cauchy problem for the porous medium equation with a variable density and a power-like rea…