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Weyl formula for the eigenvalues of the dissipative acoustic operator
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | PETKOV, Vesselin | |
| dc.date.accessioned | 2024-04-04T02:46:39Z | |
| dc.date.available | 2024-04-04T02:46:39Z | |
| dc.date.created | 2021-04-07 | |
| dc.date.issued | 2022 | |
| dc.identifier.issn | 2522-0144 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191573 | |
| dc.description.abstractEn | We study the wave equation in the exterior of a bounded domain $K$ with dissipative boundary condition $\partial_{\nu} u - \gamma(x) \partial_t u = 0$ on the boundary $\Gamma$ and $\gamma(x) > 0.$ The solutions are described by a contraction semigroup $V(t) = e^{tG}, \: t \geq 0.$ The eigenvalues $\lambda_k$ of $G$ with ${\rm Re}\: \lambda_k < 0$ yield asymptotically disappearing solutions $u(t, x) = e^{\lambda_k t} f(x)$ having exponentially decreasing global energy. We establish a Weyl formula for these eigenvalues in the case $\min_{x\in \Gamma} \gamma(x) > 1.$ For strictly convex obstacles $K$ this formula concerns all eigenvalues of $G.$ | |
| dc.language.iso | en | |
| dc.publisher | Springer | |
| dc.subject.mesh | Dissipative boundary conditions, eigenvalue asymptotics | |
| dc.title.en | Weyl formula for the eigenvalues of the dissipative acoustic operator | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1007/s40687-021-00301-3 | |
| dc.subject.hal | Mathématiques [math]/Equations aux dérivées partielles [math.AP] | |
| dc.identifier.arxiv | 2104.02341v2 | |
| bordeaux.journal | Research in the Mathematical Sciences | |
| bordeaux.page | Paper 5 | |
| bordeaux.volume | 9 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03205955 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03205955v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Research%20in%20the%20Mathematical%20Sciences&rft.date=2022&rft.volume=9&rft.issue=1&rft.spage=Paper%205&rft.epage=Paper%205&rft.eissn=2522-0144&rft.issn=2522-0144&rft.au=PETKOV,%20Vesselin&rft.genre=article |
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