15 papers
New regularity results for scalar conservation laws, and applications to a source-destination model for traffic flows on networks
Simone Dovetta, Elio Marconi, Laura V. Spinolo
We focus on entropy admissible solutions of scalar conservation laws in one space dimension and establish new regularity results with respect to time. First, we assume that the flu…
Action versus energy ground states in nonlinear Schrödinger equations
Simone Dovetta, Enrico Serra, Paolo Tilli
We investigate the relations between normalized critical points of the nonlinear Schrödinger energy functional and critical points of the corresponding action functional on the ass…
Solutions to a cubic Schrödinger system with mixed attractive and repulsive forces in a critical regime
Simone Dovetta, Angela Pistoia
We study the existence of solutions to the cubic Schrödinger system $$ -Δu_i = \sum_{j =1}^m β_{ij} u_j^2u_i + λ_i u_i\ \hbox{in}\ Ω,\ u_i=0\ \hbox{on}\ \partialΩ,\ i =1,\dots,m, $…
Uniqueness and non-uniqueness of prescribed mass NLS ground states on metric graphs
Simone Dovetta, Enrico Serra, Paolo Tilli
We consider the problem of uniqueness of ground states of prescribed mass for the Nonlinear Schrödinger Energy with power nonlinearity on noncompact metric graphs. We first establi…
Peaked and low action solutions of NLS equations on graphs with terminal edges
Simone Dovetta, Marco Ghimenti, Anna Maria Micheletti +1
We consider the nonlinear Schrödinger equation with focusing power-type nonlinearity on compact graphs with at least one terminal edge, i.e. an edge ending with a vertex of degree…
NLS ground states on metric trees: existence results and open questions
Simone Dovetta, Enrico Serra, Paolo Tilli
We consider the minimization of the NLS energy on a metric tree, either rooted or unrooted, subject to a mass constraint. With respect to the same problem on other types of metric…