Abstract and Applied Analysis

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

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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+Δ2uM(uL2(Ωt)2)Δu+0tg(ts)Δu(s)ds+αut=0 in Q^ in a noncylindrical domain of n+1(n1) 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 n1.

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Abstr. Appl. Anal., Volume 2005, Number 8 (2005), 901-919.

First available in Project Euclid: 22 December 2005

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Santos, M. L.; Ferreira, J.; Raposo, C. A. Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary. Abstr. Appl. Anal. 2005 (2005), no. 8, 901--919. doi:10.1155/AAA.2005.901. https://projecteuclid.org/euclid.aaa/1135272161

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