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Research Article | Open Access

Spectral enclosures for the damped elastic wave equation

Biagio Cassano1,2, Lucrezia Cossetti3, Luca Fanelli4( )
Dipartimento di Matematica, Università degli Studi di Bari "A. Moro", via Orabona 4, 70125 Bari, Italy
Dipartimento di Matematica e Fisica, Università degli Studi della Campania "Luigi Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy
Fakultät für Mathematik, Institut für Analysis, Karlsruher Institut für Technologie (KIT), Englerstraße 2, 76131 Karlsruhe, Germany
Ikerbasque & Departamento de Matematicas, Universidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU), Aptdo. 644, 48080, Bilbao, Spain
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Abstract

In this paper we investigate spectral properties of the damped elastic wave equation. Deducing a correspondence between the eigenvalue problem of this model and the one of Lamé operators with non self-adjoint perturbations, we provide quantitative bounds on the location of the point spectrum in terms of suitable norms of the damping coefficient.

Keywords

damped elastic wave equationLamé operatorsnon self-adjoint operatorsspectral enclosures

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Mathematics in Engineering
Volume 4 Issue 6,
December 2022
Pages 1-10
DOI: 10.3934/mine.2022052

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Cassano B, Cossetti L, Fanelli L. Spectral enclosures for the damped elastic wave equation. Mathematics in Engineering, 2022, 4(6): 1-10. https://doi.org/10.3934/mine.2022052

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Received: 10 August 2021
Accepted: 04 November 2021
Published: 15 December 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)