Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2017; 54(4): 1457-1470

Online first article July 10, 2017      Printed July 31, 2017

https://doi.org/10.4134/BKMS.b160631

Copyright © The Korean Mathematical Society.

Stabilization of viscoelastic wave equation with variable coefficients and a delay term in the internal feedback

Fei Liang

Xi An University of Science and Technology

Abstract

In this paper, we consider the stabilization of the viscoelastic wave equation with variable coefficients in a bounded domain with smooth boundary, subject to linear dissipative internal feedback with a delay. Our stabilization result is mainly based on the use of the Riemannian geometry methods and Lyapunov functional techniques.

Keywords: viscoelastic wave equation, delay in internal feedback, the Riemannian geometry

MSC numbers: 93D15, 35L05, 35L70

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