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In this paper we consider a free boundary problem of superconductivity. 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 $$\vec H$$ is divergence free and satisfies the heat equation, whereas on the interface Γ(t), curl $$\vec H \times \vec n = - V_n \vec H, where \vec n$$ is the normal of Γ(t) andV n is the velocity of Γ(t) in the direction of $$\vec n; further, \left| {\vec H} \right| = H_C $$ (constant) on Γ(t). Here our result consists of two parts: the first part is for the fixed boundary problem in 3-dimensional case with curl boundary condition, which has a unique global classical solution; the second part is for the free boundary problem in 2-dimensional case, a unique classical solution locally in time is established by Newton’s iteration method.
Acta Mathematicae Applicatae Sinica – Springer Journals
Published: Jul 3, 2007
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