6 citations · 19 across the 55 of their papers we have counts for
63 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…
Nonexistence results for the semilinear wave equation on graphs
Dario Daniele Monticelli, Fabio Punzo, Jacopo Somaglia
We investigate the semilinear wave equation with potential on weighted graphs. We establish sufficient conditions for the nonexistence of global-in-time solutions. Both nonnegative…
Relaxed uniqueness conditions for the parabolic Schrodinger equation on Riemannian manifolds
Fabio Punzo
We study uniqueness for solutions to the Cauchy problem associated with the parabolic Schrödinger equation on complete noncompact Riemannian manifolds, under suitable integral cond…
Extinction and propagation phenomena for semilinear parabolic equations on metric trees
Fabio Punzo, Alberto Tesei
We study the Cauchy-Neumann problem on a regular metric tree T for the semilinear heat equation with forcing term of KPP type. Propagation and extinction of solutions, as well as a…
A Liouville-type property for degenerate-elliptic equations modeled on Hörmander vector fields
Stefano Biagi, Dario Daniele Monticelli, Fabio Punzo
We obtain Liouville type theorems for degenerate elliptic equation with a drift term and a potential. The diffusion is driven by Hörmander operators. We show that the conditions im…
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 a semilinear parabolic equation with time-dependent source term on infinite graphs
Fabio Punzo, Alessandro Sacco
We are concerned with semilinear parabolic equations, with a time-dependent source term of the form with , posed on an infinite graph. We assume that the bottom of t…
Monotonicity results for semilinear parabolic equations on metric graphs
Fabio Punzo, Alberto Tesei
We prove monotonicity results for semilinear parabolic problems on locally finite connected metric graphs. Applications to regular metric trees are discussed.
Uniqueness for the Schrödinger Equation on Graphs with Potential Vanishing at Infinity
Fabio Punzo, Marcello Svagna
We investigate the uniqueness, in suitable weighted spaces, of solutions to the Schrödinger equation with a potential, posed on infinite graphs. The potential can tend to…
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 …
Global solutions to semilinear parabolic equations driven by mixed local-nonlocal operators
Stefano Biagi, Fabio Punzo, Eugenio Vecchi
We are concerned with the Cauchy problem for the semilinear parabolic equation driven by the mixed local-nonlocal operator , with a power-like source term.…
Phragmèn-Lindelöf type theorems for elliptic equations on infinite graphs
Stefano Biagi, Fabio Punzo
We investigate the validity of the Phragmèn-Lindelöf principle for a class of elliptic equations with a potential, posed on infinite graphs. Consequently, we get uniqueness, in the…
Nonexistence of solutions to parabolic problems with a potential on weighted graphs
Dario D. Monticelli, Fabio Punzo, Jacopo Somaglia
We investigate nonexistence of nontrivial nonnegative solutions to a class of semilinear parabolic equations with a positive potential, posed on weighted graphs. Assuming an upper…
The porous medium equation on noncompact manifolds with nonnegative Ricci curvature: a Green function approach
Gabriele Grillo, Dario D. Monticelli, Fabio Punzo
We consider the porous medium equation (PME) on complete noncompact manifolds of nonnegative Ricci curvature. We require nonparabolicity of the manifold and construct a natural…
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…
Nonexistence results for semilinear elliptic equations on weighted graphs
Dario Daniele Monticelli, Fabio Punzo, Jacopo Somaglia
We study semilinear elliptic inequalities with a potential on infinite graphs. Given a distance on the graph, we assume an upper bound on its Laplacian, and a growth condition on a…
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…
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…
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 $…
Global existence for reaction-diffusion evolution equations driven by the -Laplacian on manifolds
Gabriele Grillo, Giulia Meglioli, Fabio Punzo
We consider reaction-diffusion equations driven by the -Laplacian on noncompact, infinite volume manifolds assumed to support the Sobolev inequality and, in some cases, to have…
Blow-up for semilinear parabolic equations in cones of the hyperbolic space
Dario D. Monticelli, Fabio Punzo
We investigate existence and nonexistence of global in time nonnegative solutions to the semilinear heat equation, with a reaction term of the type ($μ\in\mathbb{R}, p>…
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.
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…