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16 October 2005 Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary
M. L. Santos, J. Ferreira, C. A. Raposo
Abstr. Appl. Anal. 2005(8): 901-919 (16 October 2005). DOI: 10.1155/AAA.2005.901

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+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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M. L. Santos. J. Ferreira. C. A. Raposo. "Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary." Abstr. Appl. Anal. 2005 (8) 901 - 919, 16 October 2005. https://doi.org/10.1155/AAA.2005.901

Information

Published: 16 October 2005
First available in Project Euclid: 22 December 2005

zbMATH: 1092.35068
MathSciNet: MR2201923
Digital Object Identifier: 10.1155/AAA.2005.901

Rights: Copyright © 2005 Hindawi

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Vol.2005 • No. 8 • 16 October 2005
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