By gradually decreasing the ambient magnetic field, under isothermal conditions, a superconductor material (of “type I”) will develop two phases separated by a thin 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
$\vec{H}\times n=-V_{n}\vec{H}$
where n is the normal and Vn the velocity of Γ(t); further,
$|\vec{H}|=H_{c}$
(constant) on Γ(t). This free boundary problem is studied in the present paper. Existence, uniqueness and asymptotic behavior are established under assumptions which enable us to reduce the 3-dimensional problem to a problem depending on essentially one-dimensional space variable.
