Homogenization of a parabolic model of ferromagnetism

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:250

Article

Visintin, Augusto

关键词: Monotone operators;    Homogenization;    Two-scale convergence;    Ferromagnetism;    Gamma-convergence;   

DOI  :  10.1016/j.jde.2010.09.016

来源: Elsevier

【 摘 要 】

This work deals with the homogenization of hysteresis-free processes in ferromagnetic composites. A degenerate, quasilinear, parabolic equation is derived by coupling the Maxwell-Ohm system without displacement current with a nonlinear constitutive law: partial derivative(B) over bar/partial derivative t + curl{A(x/epsilon).curl (H) over tilde} = curl (E) over bar (a), (B) over bar is an element of (alpha) over bar ((H) over bar, x/epsilon). Here A is a periodic positive-definite matrix, (alpha) over bar(.,gamma) is maximal monotone and periodic in y, (E) over bar (a) is an applied field, and epsilon > 0. An associated initial- and boundary-value problem is represented by a minimization principle via an idea of Fitzpatrick. As epsilon -> 0 a two-scale problem is obtained via two-scale convergence, and an equivalent coarse-scale formulation is derived. This homogenization result is then retrieved via Gamma-convergence, and the continuity of the solution with respect to the operator (alpha) over bar and the matrix A is also proved. This is then extended to some relaxation dynamics. (C) 2010 Elsevier Inc. All rights reserved.

【 授权许可】

Free