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January  2007, 7(1): 87-100. doi: 10.3934/dcdsb.2007.7.87

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, United States
2. 

Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

Received  November 2005 Revised  August 2006 Published  October 2006

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: 35Q6.
Citation: Carlos J. Garcia-Cervera, Xiao-Ping Wang. Spin-polarized transport: Existence of weak solutions. Discrete and Continuous Dynamical Systems - B, 2007, 7 (1) : 87-100. doi: 10.3934/dcdsb.2007.7.87
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