Variational approach to homogenization of doubly-nonlinear flow in a periodic structure. (June 2015)

• Record Type: Journal Article
• Authors: Nandakumaran, A.K.; Visintin, Augusto
• Is Part Of: Nonlinear analysis. Volume 120(2015)
• Page Start: 14
• Page End: 29
• Publication Date: 2015-06
• Subjects: 35B27 -- 35K60 -- 49J40 -- 78M40; Homogenization -- Doubly nonlinear flow -- Fitzpatrick theory -- Maximal monotone operators -- Two-scale convergence; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.02.010
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This work deals with the homogenization of an initial- and boundary-value problem for the doubly-nonlinear system (0.1) D t w − ∇ ⋅ z → = g ( x, t, x / ε ) (0.2) w ∈ α ( u, x / ε ) (0.3) z → ∈ γ → ( ∇ u, x / ε ) . Here ε is a positive parameter; α and γ → are maximal monotone with respect to the first variable and periodic with respect to the second one. The inclusions(0.2) and(0.3) are here formulated as null-minimization principles, via the theory of Fitzpatrick [MR 1009594]. As ε → 0, a two-scale formulation is derived via Nguetseng's notion of two-scale convergence, and a (single-scale) homogenized problem is then retrieved.