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On Boundary Stability of Wave Equations with Variable Coefficients

On Boundary Stability of Wave Equations with Variable Coefficients In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua [2] are generalized to the variable coefficient case by some computational techniques in Riemannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

On Boundary Stability of Wave Equations with Variable Coefficients

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Publisher
Springer Journals
Copyright
Copyright © 2002 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s102550200061
Publisher site
See Article on Publisher Site

Abstract

In this paper, we consider the boundary stabilization of the wave equation with variable coefficients by Riemannian geometry method subject to a different geometric condition which is motivated by the geometric multiplier identities. Several (multiplier) identities (inequalities) which have been built for constant wave equation by Kormornik and Zuazua [2] are generalized to the variable coefficient case by some computational techniques in Riemannian geometry, so that the precise estimates on the exponential decay rate are derived from those inequalities. Also, the exponential decay for the solutions of semilinear wave equation with variable coefficients is obtained under natural growth and sign assumptions on the nonlinearity. Our method is rather general and can be adapted to other evolution systems with variable coefficients (e.g. elasticity plates) as well.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2002

References