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Eigenvalues and resonances of dissipative acoustic operator for strictly convex obstacles
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| dc.date.accessioned | 2024-04-04T02:32:55Z | |
| dc.date.available | 2024-04-04T02:32:55Z | |
| dc.date.created | 2023-10-03 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190427 | |
| dc.description.abstractEn | We examine the wave equation in the exterior of a strictly convex bounded domain $K$ with dissipative boundary condition $\partial_{\nu} u - \gamma(x) \partial_t u = 0$ on the boundary $\Gamma$ and $0 < \gamma(x) <1, \:\forall x \in \Gamma.$ The solutions are described by a contraction semigroup $V(t) = e^{tG}, \: t \geq 0.$ The poles $\lambda$ of the meromorphic incoming resolvent $(G - \lambda)^{-1}: \: {\mathcal H}_{comp} \rightarrow {\mathcal D}_{loc}$ are eigenvalues of G if ${\rm Re}\: \lambda < 0$ and incoming resonances if ${\rm Re}\: \lambda > 0$. We obtain sharper results for the location of the eigenvalues of $G$ and incoming resonances in $\Lambda = \{\lambda \in {\mathbb C}:\: |{\rm Re}\: \lambda| \leq C_2(1 + |{\rm Im}\:\lambda|)^{-2},\: |{\rm Im}\:\lambda| \geq A_2 > 1\}$ and we prove a Weyl formula for their asymptotic. For $K = \{x \in {\mathbb R}^3:\:|x| \leq 1\}$ and $\gamma$ constant we show that $G$ has no eigenvalues so the Weyl formula concerns only the incoming resonances. | |
| dc.language.iso | en | |
| dc.subject.en | dissipative boundary conditions | |
| dc.subject.en | asymptotic of eigenvalues | |
| dc.subject.en | incoming resonances | |
| dc.title.en | Eigenvalues and resonances of dissipative acoustic operator for strictly convex obstacles | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math] | |
| dc.identifier.arxiv | 2310.01192.math.AP | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-04265626 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-04265626v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=PETKOV,%20Vesselin&rft.genre=preprint |
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