Spectral determinant for the wave equation on an interval with Dirac damping

David Krejcirik; Jiri Lipovsky

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arXiv · 2404.11992

Spectral determinant for the wave equation on an interval with Dirac damping

David Krejcirik·Jiri Lipovsky

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Abstract

A closed formula for the spectral determinant for the wave equation on a bounded interval, subject to Dirichlet boundary conditions and an $\alpha$-multiple of the Dirac $\delta$-type damping, is derived. Depending on the choice of the branch cut of the logarithm used in its definition, the spectral determinant diverges either for $\alpha =2$ or $\alpha=-2$.

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BibTeX RIS

David Krejcirik, Jiri Lipovsky. 2024-04-18. Spectral determinant for the wave equation on an interval with Dirac damping. https://arxiv.org/abs/2404.11992

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