Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary

M. L. Santos, J. Ferreira and C. A. Raposo

Abstract and Applied Analysis, 2005, vol. 2005, issue 8, 901-919

Abstract: We prove the exponential decay in the case n > 2, as time goes to infinity, of regular solutions for the nonlinear beam equation with memory and weak damping utt + Δ2u−M(‖∇u‖L2(Ωt)2)Δu+∫0tg(t−s)Δu(s)ds+αut=0 in Q∧ in a noncylindrical domain of ℝn+1(n ≥ 1) under suitable hypothesis on the scalar functions M and g, and where α is a positive constant. We establish existence and uniqueness of regular solutions for any n ≥ 1.

Date: 2005
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https://doi.org/10.1155/AAA.2005.901

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2005:y:2005:i:8:p:901-919

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