EVOLUTION OF MIXED-STATE REGIONS IN TYPE-II SUPERCONDUCTORS

A mean-field model for dynamics of superconducting vortices is studied . The model, consisting of an elliptic equation coupled with a hyperbo lic equation with discontinuous initial data, is formulated as a syste m of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C1+alpha(<(Ohm)over bar>(0)) for all t > 0, where Ohm(0) is the initial vortex region that is assumed to be in C1+alpha. Consequently, for any time t, the vortex region Omega(t) is of C1+alpha, and the vorticity is in C-alpha(<(Omega)over bar>(t)).