11 papers
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 de…
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…
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 con…
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 i…