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

Krejčiřík, David; Royer, Julien

doi:10.1090/proc/16412

Spectrum of the wave equation with Dirac damping on a non-compact star graph
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by David Krejčiřík and Julien Royer;

Proc. Amer. Math. Soc. 151 (2023), 4673-4691

DOI: https://doi.org/10.1090/proc/16412

Published electronically: May 12, 2023

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Abstract:

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.

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