Spectral enclosures for the damped elastic wave equation

Biagio Cassano; Lucrezia Cossetti; Luca Fanelli; Biagio Cassano; Lucrezia Cossetti; Luca Fanelli

doi:10.3934/mine.2022052

Mathematics in Engineering

2022, Volume 4, Issue 6: 1-10. doi: 10.3934/mine.2022052

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Spectral enclosures for the damped elastic wave equation

1.
Dipartimento di Matematica, Università degli Studi di Bari "A. Moro", via Orabona 4, 70125 Bari, Italy
2.
Dipartimento di Matematica e Fisica, Università degli Studi della Campania "Luigi Vanvitelli", Viale Lincoln 5, 81100 Caserta, Italy
3.
Fakultät für Mathematik, Institut für Analysis, Karlsruher Institut für Technologie (KIT), Englerstraße 2, 76131 Karlsruhe, Germany
4.
Ikerbasque & Departamento de Matematicas, Universidad del País Vasco/Euskal Herriko Unibertsitatea (UPV/EHU), Aptdo. 644, 48080, Bilbao, Spain

Received: 10 August 2021 Accepted: 04 November 2021 Published: 23 November 2021

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.
- damped elastic wave equation,
- Lamé operators,
- non self-adjoint operators,
- spectral enclosures
Citation: Biagio Cassano, Lucrezia Cossetti, Luca Fanelli. Spectral enclosures for the damped elastic wave equation[J]. Mathematics in Engineering, 2022, 4(6): 1-10. doi: 10.3934/mine.2022052

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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.

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