کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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6415101 | 1334935 | 2015 | 46 صفحه PDF | دانلود رایگان |
We address the deterministic homogenization, in the general context of ergodic algebras, of a doubly nonlinear problem which generalizes the well known Stefan model, and includes the classical porous medium equation. It may be represented by the differential inclusion, for a real-valued function u(x,t),ââtâuΨ(x/ε,x,u)ââxâ âηÏ(x/ε,x,t,u,âu)âf(x/ε,x,t,u), on a bounded domain ΩâRn, tâ(0,T), together with initial-boundary conditions, where Ψ(z,x,â ) is strictly convex and Ï(z,x,t,u,â ) is a C1 convex function, both with quadratic growth, satisfying some additional technical hypotheses. As functions of the oscillatory variable, Ψ(â ,x,u),Ï(â ,x,t,u,η) and f(â ,x,t,u) belong to the generalized Besicovitch space B2 associated with an arbitrary ergodic algebra A. The periodic case was addressed by Visintin (2007), based on the two-scale convergence technique. Visintin's analysis for the periodic case relies heavily on the possibility of reducing two-scale convergence to the usual L2 convergence in the Cartesian product Î ÃRn, where Î is the periodic cell. This reduction is no longer possible in the case of a general ergodic algebra. To overcome this difficulty, we make essential use of the concept of two-scale Young measures for algebras with mean value, associated with bounded sequences in L2.
Journal: Journal of Functional Analysis - Volume 268, Issue 11, 1 June 2015, Pages 3232-3277