Spectrum of the wave equation with Dirac damping on a non-compact star graph

David Krejcirik (1) , Julien Royer (2)

1 CTU - Czech Technical University in Prague
2 IMT - Institut de Mathématiques de Toulouse UMR5219

We consider the wave equation on non-compact star graphs, subject to a distributional damping defined through a Robin-type vertex condition with complex coupling. It is shown that the non-self-adjoint generator of the evolution problem admits an abrupt change in its spectral properties for a special coupling related to the number of graph edges. As an application, we show that the evolution problem is highly unstable for the critical couplings. The relationship with the Dirac equation in non-relativistic quantum mechanics is also mentioned.

Domaines: Physique mathématique [math-ph]

David Krejcirik, Julien Royer. Spectrum of the wave equation with Dirac damping on a non-compact star graph. 2022. ⟨hal-03652993⟩