Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity
Gabriel Nguetseng,1Hubert Nnang,2and Nils Svanstedt3
Academic Editor: Lars-Erik Persson
Received01 Dec 2007
Abstract
The present work is devoted to the study of homogenization of the weakly damped wave equation ∫Ωρε∂2uε∂t2(t)⋅υdx+2ε2μ∫ΩfεEij(∂uε∂t(t))Eij(υ)dx+ε2λ∫Ωfεdiv(∂uε∂t(t))divυdx+ϑ∫Ωfεdiv(uε(t))divυdx=∫Ωf(t)⋅υdxforallυ=(υ1,υ2,υ3)∈Vε(0<t<T), with initial conditions uε(0)=∂uε∂t(0)=ω(theorigininℝ3). Convergence homogenization results are achieved using the two-scale convergence theory.