Geodesic
Stabilization of the wave equation with variable coefficients and a dynamical boundary control
Electronic Journal of Differential Equations, Tome 2016 (2016).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article we consider the boundary stabilization of the wave equation with variable coefficients and a dynamical Neumann boundary control. The dynamics on the boundary comes from the acceleration terms which can not be ignored in some physical applications. It has been known that addition of dynamics to the boundary may change drastically the stability properties of the underlying system. In this paper by applying a boundary feedback control we obtain the exponential decay for the solutions. Our proof relies on the Geometric multiplier skills and the energy perturbed approach.
Classification : 34H05, 35L05, 49K25, 93C20, 93D15
Keywords: exponential decay, wave equation with variable coefficients, dynamical boundary control 
@article{EJDE_2016__2016__a32,
     author = {Zhang, Zhifei},
     title = {Stabilization of the wave equation with variable coefficients and a dynamical boundary control},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2016},
     year = {2016},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a32/}
}
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Zhang, Zhifei. Stabilization of the wave equation with variable coefficients and a dynamical boundary control. Electronic Journal of Differential Equations, Tome 2016 (2016). http://geodesic.mathdoc.fr/item/EJDE_2016__2016__a32/