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, 1-19

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 u t t + Δ 2 u − M ( ‖ ∇ u ‖ L 2 ( Ω t ) 2 ) Δ u + ∫ 0 t g ( t − s ) Δ u ( s ) d s + α u t = 0 in Q ^ in a noncylindrical domain of ℝ n + 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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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:693727

DOI: 10.1155/AAA.2005.901

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