Stability of the wave equation with localized Kelvin-Voigt damping and  boundary delay feedback

Serge Nicaise; Cristina Pignotti

doi:10.3934/dcdss.2016029

Article Contents

2016, Volume 9, Issue 3: 791-813. Doi: 10.3934/dcdss.2016029

This issue Previous Article Semigroup-theoretic approach to identification of linear diffusion coefficients Next Article A symmetry result for degenerate elliptic equations on the Wiener space with nonlinear boundary conditions and applications

Stability of the wave equation with localized Kelvin-Voigt damping and boundary delay feedback

Serge Nicaise^1, and
Cristina Pignotti^2,

1.
Université de Valenciennes et du Hainaut Cambrésis, LAMAV and FR CNRS 2956, Le Mont Houy, Institut des Sciences et Techniques de Valenciennes, 59313 Valenciennes Cedex 9
2.
Dipartimento di Matematica Pura e Applicata, Università di L'Aquila, Via Vetoio, Loc. Coppito, 67010 L'Aquila

Received: February 28, 2015

Revised: June 30, 2015

Published: May 2016

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Abstract

We study the stabilization problem for the wave equation with localized Kelvin--Voigt damping and mixed boundary condition with time delay. By using a frequency domain approach we show that, under an appropriate condition between the internal damping and the boundary feedback, an exponential stability result holds. In this sense, this extends the result of [19] where, in a more general setting, the case of distributed structural damping is considered.

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Mathematics Subject Classification: Primary: 35L05; Secondary: 93D15.

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References

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