On a Degenerate Evolution System Associated with the Bean Critical-State for Type II Superconductors

Abstract

We study a degenerate evolution system containing the $p$-curl system in a bounded domain with initial and boundary conditions for the magnetic field $\mathbf{H}$ under the influence of a system force $\mathbf{F}$. This is concerned with an approximation of Bean’s critical-state model for type II superconductors. We will show the existence, uniqueness, and regularity of solutions. Moreover we will get the properties of the limit solution as $p\to \mathrm{\infty }$.