The damped wave equation with unbounded damping

Freitas, Pedro; Siegl, Petr; Tretter, Christiane (2018). The damped wave equation with unbounded damping. Journal of differential equations, 264(12), pp. 7023-7054. Elsevier 10.1016/j.jde.2018.02.010

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We analyze new phenomena arising in linear damped wave equations on unbounded domains when the damping is allowed to become unbounded at infinity. We prove the generation of a contraction semigroup, study the relation between the spectra of the semigroup generator and the associated quadratic operator function, the convergence of non-real eigenvalues in the asymptotic regime of diverging damping on a subdomain, and we investigate the appearance of essential spectrum on the negative real axis. We further show that the presence of the latter prevents exponential estimates for the semigroup and turns out to be a robust effect that cannot be easily canceled by adding a positive potential. These analytic results are illustrated by examples.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Siegl, Petr and Tretter, Christiane

Subjects:

500 Science > 510 Mathematics

ISSN:

0022-0396

Publisher:

Elsevier

Language:

English

Submitter:

Olivier Bernard Mila

Date Deposited:

15 May 2019 17:56

Last Modified:

24 Oct 2019 19:22

Publisher DOI:

10.1016/j.jde.2018.02.010

BORIS DOI:

10.7892/boris.125530

URI:

https://boris.unibe.ch/id/eprint/125530

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