Asymptotic analysis for a weakly damped wave equation with application to a problem arising in elasticity. Issue 1 (2010)

• Record Type: Journal Article
• Authors: Nguetseng Nguetseng, Gabriel Gabriel; Nnang Nnang, Hubert Hubert; Svanstedt Svanstedt, Nils Nils
• Other Names: Persson Persson Lars-Erik Lars-Erik Academic Editor.
• Is Part Of: Journal of function spaces and applications. Volume 8:Issue 1(2010)
• Page Start: 17
• Page End: 54
• Publication Date: 2010
• Subjects: Homogenization, two-scale convergence, elasticity, wave equation; Function spaces -- Periodicals; 515.73
• DOI: 10.1155/2010/291670
• Languages: English
• ISSNs: 0972-6802

Abstract

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.