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July  2002, 8(3): 781-794. doi: 10.3934/dcds.2002.8.781

A degenerate evolution system modeling bean's critical-state type-II superconductors

H. M. Yin 1, , Ben Q. Li 2, and  Jun Zou 3,

1. 

Department of Mathematics, Washington State University, Pullman, WA 99164, United States
2. 

Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164, United States
3. 

Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong, China

Received  May 2001 Revised  December 2001 Published  April 2002

In this paper we study a degenerate evolution system $\mathbf H_t +\nabla \times [|\nabla \times \mathbf H|^{p-2}\nabla \times \mathbf H]=\mathbf F$ in a bounded domain as well as its limit as $p\to \infty$ subject to appropriate initial and boundary conditions. This system governs the evolution of the magnetic field $\mathbf H$ in a conductive medium under the influence of a system force $\mathbf F$. The system is an approximation of Bean's critical-state model for type-II superconductors. The existence, uniqueness and regularity of solutions to the system are established. Moreover, it is shown that the limit of $\mathbf H(x, t)$ as $p\to \infty$ is a solution to the Bean model.
Keywords: Nonlinear evolution system, Bean's critical-state model for superconductors..
Mathematics Subject Classification: 35Q60, 35K5.
Citation: H. M. Yin, Ben Q. Li, Jun Zou. A degenerate evolution system modeling bean's critical-state type-II superconductors. Discrete and Continuous Dynamical Systems, 2002, 8 (3) : 781-794. doi: 10.3934/dcds.2002.8.781
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