The damped wave equation with singular damping

Freitas, Pedro; Hefti, Nicolas; Siegl, Petr (2020). The damped wave equation with singular damping. Proceedings of the American Mathematical Society, 148(10), pp. 4273-4284. American Mathematical Society 10.1090/proc/15063

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We analyze the spectral properties and peculiar behavior of solutions of a damped wave equation on a finite interval with a singular damping of the form α/x, α > 0. We establish the exponential stability of the semigroup for all positive α, and determine conditions for the spectrum to consist of a finite number of eigenvalues. As a consequence, we fully characterize the set of initial conditions for which there is extinction of solutions in finite time. Finally, we propose two open problems related to extremal decay rates of solutions.

Item Type:

Journal Article (Original Article)

Division/Institute:

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

UniBE Contributor:

Hefti, Nicolas Benjamin

Subjects:

500 Science > 510 Mathematics

ISSN:

0002-9939

Publisher:

American Mathematical Society

Funders:

[UNSPECIFIED] FCT (Portugal) ; [4] Swiss National Science Foundation

Projects:

[UNSPECIFIED] PTDC/MATCAL/4334/2014

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

10 Feb 2021 17:21

Last Modified:

10 Feb 2021 17:21

Publisher DOI:

10.1090/proc/15063

ArXiv ID:

2002.03440

Uncontrolled Keywords:

damped wave equation, singular damping, empty spectrum, finite- time extinction, Laguerre polynomials.

BORIS DOI:

10.48350/151270

URI:

https://boris.unibe.ch/id/eprint/151270

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