Title: Rates of decay for structural damped models with decreasing in time coefficients

Authors: Xiaojun Lu, Michael Reissig

Addresses: Department of Mathematics, Zhejiang University, 310027 Hangzhou, PR China. ' Faculty for Mathematics and Computer Science, TU Bergakademie Freiberg, Pruferstr.9, 09596 Freiberg, Germany

Abstract: The goal of this paper is to study the Cauchy problem for a family of structural damped models interpolation between classical damped wave and wave model with viscoelastic dissipation. We are interested to observe the parabolic effect in high order energy estimates, that is, decay rates depend on the order of the energy. The main tools are related to WKB-analysis. One has to apply elliptic as well as hyperbolic WKB-analysis in different parts of the extended phase space.

Keywords: decay rates; parabolic behaviour; time-dependent dissipation; WKB analysis; structural damped models; time coefficients; interpolation; damped wave models; wave modelling; viscoelastic dissipation.

DOI: 10.1504/IJDSDE.2009.028034

International Journal of Dynamical Systems and Differential Equations, 2009 Vol.2 No.1/2, pp.21 - 55

Published online: 02 Sep 2009 *

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