Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity. Issue 1 (2010) - Nguetseng Nguetseng, Gabriel Gabriel; Nnang Nnang, Hubert Hubert; Svanstedt Svanstedt, Nils Nils
Abstract : The present work is devoted to the study of homogenization of the weakly damped wave equation ∫ Ω ρ ε ∂ 2 u ε ∂ t 2 ( t ) ⋅ υ d x + 2 ε 2 μ ∫ Ω f ε E i j ( ∂ u ε ∂ t ( t ) ) E i j ( υ ) d x + ε 2 λ ∫ Ω f ε div ( ∂ u ε ∂ t ( t ) ) div υ d x + ϑ ∫ Ω f ε div ( u ε ( t ) ) div υ d x = ∫ Ω f ( t ) ⋅ υ d x for all υ = ( υ 1, υ 2, υ 3 ) ∈ V ε ( 0 < t < T ), with initial conditions u ε ( 0 ) = ∂ u ε ∂ t ( 0 ) = ω ( the origin in ℝ 3 ) . Convergence homogenization results are achieved using the two-scale convergence theory.