3 papers
math.SP2026
Two escape rates for negative eigenvalues of quantum graphs with a shrinking core
Gregory Berkolaiko, Denis Borisov, Marshall King +1
We study the negative spectrum of the Laplacian on a metric graph with general vertex matching conditions and with two length scales: a compact core whose edges have length of orde…
math.AP2026
Semigroup decay for the wave equation with unbounded damping
Antonio Arnal, Borbala Gerhat, Julien Royer +1
We study the damped wave equation with a damping coefficient which is possibly singular and unbounded at infinity. In general, zero belongs to the spectrum of the corresponding gen…
math.AP2024
A minimal mass blow-up solution on a nonlinear quantum star graph
François Genoud, Stefan Le Coz, Julien Royer
We construct a finite-time blow-up solution to the mass-critical focusing nonlinear Schrödinger equation on a metric star graph with an arbitrary number of edges. We show that all…