ΓD‐convergence for a class of quasilinear elliptic equations in thin structures
Brahim Amaziane, М. В. Гончаренко, Leonid Pankratov · Mathematical Methods in the Applied Sciences · 2005
Abstract We study the asymptotic behaviour of the solution of a stationary quasilinear elliptic problem posed in a domain Ω(ε)of asymptotically degenerating measure, i.e. meas Ω(ε)→ 0 asε→ 0, whereεis the parameter that characterizes the scale of the microstructure. We obtain the convergence of the solution and the homogenized model of the problem is constructed using the notion of convergence in domains of degenerating measure. Proofs are given using the method of local characteristics of the medium Ω(ε)associated with our problem in a variational form. Copyright © 2005 John Wiley & Sons, Ltd.