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December  2002, 1(4): 485-494. doi: 10.3934/cpaa.2002.1.485

A note on the convergence in the limit of a long wave vortex density superconductivity model to the Bean model

V. Styles 1,

1. 

Centre for Mathematical Analysis and Its Applications, School of Mathematical Scie, University of Sussex, Falmer, Brighton BN1 9QH, United Kingdom

Received  January 2001 Revised  August 2002 Published  September 2002

We show that the unique solution of the Bean model for superconductivity is the $p\to \infty$ limit of the solution to a two-dimensional vortex density model with a p-Laplacian velocity law.
Keywords: doubly degenerate nonlinear diffusion., Bean model for superconductivity.
Mathematics Subject Classification: 35Q60, 35K5.
Citation: V. Styles. A note on the convergence in the limit of a long wave vortex density superconductivity model to the Bean model. Communications on Pure & Applied Analysis, 2002, 1 (4) : 485-494. doi: 10.3934/cpaa.2002.1.485
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