Spin-polarized transport: Existence of weak solutions

Carlos J. Garcia-Cervera; Xiao-Ping Wang

doi:10.3934/dcdsb.2007.7.87

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2007, Volume 7, Issue 1: 87-100. Doi: 10.3934/dcdsb.2007.7.87

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Spin-polarized transport: Existence of weak solutions

Carlos J. Garcia-Cervera^1, and
Xiao-Ping Wang^2,

1.
Mathematics Department, South Hall, Room 6707, University of California, Santa Barbara, CA 93106
2.
Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon

Received: October 31, 2005

Revised: July 31, 2006

Published: December 2006

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Abstract

A system modeling spin-polarized transport in ferromagnetic multilayers is considered. In this model, the spin accumulation is described by a quasilinear diffusion equation with discontinuous, measurable coefficients. This equation is coupled to the Landau-Lifshitz-Gilbert equation, a nonlinear, nonlocal equation describing the precession of the magnetization in the ferromagnetic layers. The global existence of weak solutions is proved.

Keywords:

Micromagnetics; Landau-Lifshitz; Weak Solutions.

Mathematics Subject Classification: Primary: 35R05, 58J35; Secondary: 35Q60.

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