Nonlinear Degenerating Parabolic Problem from the Theory of Type II Superconductors

摘要

A boundary value problem for a nonlinear partial differential equation is studied. This problem arises as a model for the current distribution in a multifilamentary wire in which the filaments consist of a type II superconducting material. The equation is ostensibly of parabolic type, but displays two types of degeneracy. The derivation of the model is explained. The existence and the uniqueness of a solution of the boundary value problem are proved. A comparison principle and some regularity results for its solution are established. The paper concludes with a brief discussion of the physical interpretation of the different results.