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) |
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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: |
05 Dec 2022 15:45 |
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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