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General Decay of Solutions of a Nonlinear System of Viscoelastic Equations

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Abstract

In this paper we consider a system of two coupled viscoelastic equations with Dirichlet boundary condition which describes the interaction between two different fields arising in viscoelasticity. For certain class of relaxation functions and certain initial data, we prove that the decay rate of the solution energy is similar to that of relaxation functions which is not necessarily of exponential or polynomial type. This result improves earlier one of Messaoudi and Tatar (Appl. Anal. 87(3):247–263, 2008) and extends some existing results concerning the general decay for a single equation to the case of a system.

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  1. College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing, 210044, China

    Wenjun Liu

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  1. Wenjun Liu
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Correspondence to Wenjun Liu.

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Liu, W. General Decay of Solutions of a Nonlinear System of Viscoelastic Equations. Acta Appl Math 110, 153–165 (2010). https://doi.org/10.1007/s10440-008-9391-3

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