Spectral analysis and best decay rate of the wave propagator on the tadpole graph

2024/04/28 by Kaïs Ammari, Ammari, Kaïs, Rachid Assel +3 · 1 citation
Mathematics · #34B45 #34L25 #35B20 #35B40 #47A60 #Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2404.18295

openalex publication_date 2024/04/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the damped wave semigroup on the tadpole graph \mathcal R. We first give a meticulous spectral analysis, followed by a judicious decomposition of the resolvent's kernel. As a consequence, and by showing that the generalized eigenfunctions form a Riesz basis of some subspace of the energy space H, we establish the exponential decay of the corresponding energy, with the optimal decay rate dictated by the spectral abscissa of the relevant operator.

Cited by

• Ground States of the Nonlinear Schrödinger Equation on the Tadpole Graph with a Repulsive Delta Vertex Condition

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