On a p-Laplacian type of evolution system and applications to the bean model in the type-II superconductivity theory

In this paper we study the Cauchy problem for a p-Laplacian type of evoluti on system H-t + del x [\del x H\(p-2)del x H] = F. This system governs the evolution of a magnetic field H, where the displacement currently is neglec ted and the electrical resistivity is assumed to be some power of the curre nt density. The existence, uniqueness, and regularity of solutions to the s ystem are established. Furthermore, it is shown that the limit solution as the power p --> infinity solves the problem of Bean's model in the type-TI superconductivity theory. The result provides us information about how the superconductor material under the external force becomes the normal conduct or and vice versa. It also provides an effective method for finding numeric al solutions to Bean's model.