Boundary Stabilization and a Problem of Transmission for a System of Propagation of Sound

We consider a transmission problem for a model describing the evolution of sound in a compressible fluid. Assuming that dissipative mechanisms of memory type are effective in part of the boundary, the coefficients are piecewise constants and suitable geometric conditions on the domain and the interf...

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Bibliographic Details
Published inFunkcialaj Ekvacioj Vol. 49; no. 1; pp. 107 - 132
Main Authors Kapitonov, Boris V., Menzala, G. Perla
Format Journal Article
LanguageEnglish
Published Tokyo Division of Functional Equations, The Mathematical Society of Japan 2006
Japan Science and Technology Agency
Subjects
Boundary stabilization
Multiplier method
Transmission problem
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Summary:We consider a transmission problem for a model describing the evolution of sound in a compressible fluid. Assuming that dissipative mechanisms of memory type are effective in part of the boundary, the coefficients are piecewise constants and suitable geometric conditions on the domain and the interfaces, we prove that the total energy associated with the model decays exponentially fast as t → + ∞.
ISSN:0532-8721
DOI:10.1619/fesi.49.107