GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS

doi:10.1016/S0252-9602(11)60329-9

Abstract

Abstract:

The initial boundary value problem for a viscoelastic equation

|u_t|^ρ u_tt -Δu-Δu_tt+∫^t₀g(t-s)Δu(s)ds+|^mu_t| u_t= |u|^p u

in a bounded domain is considered, where ρ,m,p > 0 and g is a nonnegative and decaying
function. The general uniform decay of solution energy is discussed under some conditions
on the relaxation function g and the initial data by adopting the method of [14, 15, 19].
This work generalizes and improves earlier results in the literature.

Key words: global existence, asymptotic behavior, general decay

CLC Number:

35B35

WU Shun-Tang. GENERAL DECAY OF SOLUTIONS FOR A VISCOELASTIC EQUATION WITH NONLINEAR DAMPING AND SOURCE TERMS[J].Acta mathematica scientia,Series B, 2011, 31(4): 1436-1448.

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