# A free boundary problem of type-I superconductivity

A free boundary problem of type-I superconductivity 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# A free boundary problem of type-I superconductivity

, Volume 14 (1) – Jul 3, 2007
10 pages

/lp/springer-journals/a-free-boundary-problem-of-type-i-superconductivity-ExJKmtv2C9
Publisher
Springer Journals
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02677348
Publisher site
See Article on Publisher Site

### Abstract

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.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 3, 2007

### References

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