American Institute of Mathematical Sciences

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

 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.
Citation: H. M. Yin, Ben Q. Li, Jun Zou. A degenerate evolution system modeling bean's critical-state type-II superconductors. Discrete & Continuous Dynamical Systems - A, 2002, 8 (3) : 781-794. doi: 10.3934/dcds.2002.8.781
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