Stabilization of hyperbolic problems with localized damping in unbounded domains

We are concerned with stability issues for hyperbolic problems in unbounded domains. We consider the Klein-Gordon equation posed in the whole N-dimensional Euclidian space RN and also the wave equation posed in unbounded domains with finite measure. The goal is to remove the damping at infinity. Pre...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2024-09, Vol.537 (1), p.128256, Article 128256
Main Authors: Cavalcanti, M.M., Domingos Cavalcanti, V.N., Gonzalez Martinez, Victor H., Druziani Marchiori, Talita, Vicente, A.
Format: Article
Language:English
Subjects:
Klein-Gordon equation
Localized frictional damping
Microlocal analysis
Stability
Unbounded domain with finite measure
Wave equation
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Summary:We are concerned with stability issues for hyperbolic problems in unbounded domains. We consider the Klein-Gordon equation posed in the whole N-dimensional Euclidian space RN and also the wave equation posed in unbounded domains with finite measure. The goal is to remove the damping at infinity. Precisely, given a positive real number M>0, we construct a region Ξ free of damping, with finite measure, such that Ξ is globally distributed. To establish our results we use the microlocal analysis theory combined with Egorov's theorem.
ISSN:0022-247X
DOI:10.1016/j.jmaa.2024.128256