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arXiv · 2404.18295

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

Kaïs Ammari·Rachid Assel·Mouez Dimassi
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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 $\mathcal{H}$, we establish the exponential decay of the corresponding energy, with the optimal decay rate dictated by the spectral abscissa of the relevant operator.

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Kaïs Ammari, Rachid Assel, Mouez Dimassi. 2024-04-28. Spectral analysis and best decay rate of the wave propagator on the tadpole graph. https://arxiv.org/abs/2404.18295

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