Abstract and Applied Analysis
Volume 2005 (2005), Issue 8, Pages 901-919
doi:10.1155/AAA.2005.901
Existence and uniform decay for a nonlinear beam equation with nonlinearity of Kirchhoff type in domains with moving boundary
M.L. Santos1
, J. Ferreira2
and C.A. Raposo2
1Departamento de Matemática, Universidade Federal do Pará, Campus Universitário do Guamá, Rua Augusto Corrêa 01, Pará CEP 66075-110, Brazil
2Departamento de Matemática, Estatística e Ciências da Computaçäo, Universidade Federal de São João del-Rei (UFSJ), Praça Frei Orlando 170, São João del-Rei CEP 36300-000, Minas Gerais, Brazil
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.