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

H. M. Yin; Ben Q. Li; Jun Zou

doi:10.3934/dcds.2002.8.781

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2002, Volume 8, Issue 3: 781-794. Doi: 10.3934/dcds.2002.8.781

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

1.
Department of Mathematics, Washington State University, Pullman, WA 99164
2.
Department of Mechanical and Materials Engineering, Washington State University, Pullman, WA 99164
3.
Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong

Received: April 30, 2001

Revised: November 30, 2001

Published: June 2002

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Abstract

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, 35K50.

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