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Decay estimates for dissipative wave equations in inhomogeneous media
JI Shu-Guan
College of Mathematics, Jilin University, Changchun 130012
*Correspondence author
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Funding: Partially supported by NSFC （No.11171130 and 11322105）, SRFDP （No.20120061110004）, National 973 Program of China（No.2012CB821200 and 2013CB834102）, NCET （No.12-0228）
Opened online:24 June 2016
Accepted by: none
Citation: JI Shu-Guan.Decay estimates for dissipative wave equations in inhomogeneous media[OL]. [24 June 2016] http://en.paper.edu.cn/en_releasepaper/content/4697305
 
 
This paper is concerned with the long time behavior of one-dimensional dissipativewave equation with $x$-dependent coefficients $u(x)y_{tt}-(u(x)y_x)_x+a(x)y_t=0$. Such a model arises from the vibrations of an inhomogeneous string and the propagationof seismic waves in nonisotropic media subject to a viscous damping. Meanwhile, it is also a natural reduction model for the $n$-dimensional wave equation in inhomogeneous radially symmetric media.By using the multiplier method, we establish the power decay estimates for the energy and the $L^2$-norm of solutions.
Keywords:Wave equation, damping, inhomogeneous media, decay estimates.
 
 
 

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