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))div υdx+ϑ∫Ωfεdiv(uε(t))divυdx=∫Ωf(t)⋅υdx  for all υ=(υ1,υ2,υ3)∈Vε(0<t<T), with initial conditions uε(0)=∂uε∂t(0)=ω (the origin in ℝ3). Convergence homogenization results are achieved using the two-scale convergence theory.