6 citations · 19 across the 55 of their papers we have counts for
8 papers · 1 filter
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.