Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity

The present work is devoted to the study of homogenization of the weakly damped wave equation ∫ ω ρ ε∂ 2u ε/∂t 2(t) · vdx + 2ε 2μ ∫ ωfε e ij(∂ u ε/∂t(t))e ij(v)dx + ε 2λ ∫ ωfε div(∂u ε/∂t(t))divdx + θ ∫ ωfε div(u ε(t))divdx = ∫ ωf(t) · vdx for all v = (v 1,v 2,v 3) ∈ v ε (0<t<t),with initial conditions u ε(0) = ∂u ε/∂t(0) = ω (the origin in ℝ 3m). convergence homogenization results are achieved using the two-scale convergence theory. copyright © 2010 hindawi publishing corporation.