Mathematics Commons^™

Evolution Of Mixed-State Regions In Type-Ii Superconductors, Chaocheng Huang, Tom Svobodny

Mathematics and Statistics Faculty Publications

A mean-field model for dynamics of superconducting vortices is studied. The model, consisting of an elliptic equation coupled with a hyperbolic equation with discontinuous initial data, is formulated as a system of nonlocal integrodifferential equations. We show that there exists a unique classical solution in C^1+α(Ω₀) for all t > Ω, where Ω₀ is the initial vortex region that is assumed to be in C^1+α. Consequently, for any time t, the vortex region Ω_t is of C^1+α, and the vorticity is in C^α(Ω_t).