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A note on the classical solution of a two-dimensional superconductor free boundary problem

Published online by Cambridge University Press:  26 September 2008

Fahuai Yi
Fahuai Yi
Affiliation:
Department of Mathematics, Suzhou University, Suzhou 215006, China
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Abstract

In this paper we consider a superconductor free boundary problem. Under isothermal conditions, a superconductor material (of ‘type I’) will develop two phases separated by a sharp interface Γ(t). In the ‘normal’ conducting phase the magnetic field is divergence free and satisfies the heat equation, whereas on the interface Γ(t), curl , where n is the normal and Vn is the velocity of Γ(t) in the direction of n; further, (constant) on Γ(t). Existence and uniqueness of a classical solution locally in time are established by Newton's iteration method under assumptions which enable us to reduce the 3-dimensional problem to a problem depending on essentially two space variables.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 7 , Issue 2 , April 1996 , pp. 113 - 118
Copyright
Copyright © Cambridge University Press 1996

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References

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