On a degenerate parabolic system

In this paper we study a degenerate parabolic systemUt−Δ(|U|m−1U)=0,where U(x,t)=(u1,u2,…,ul) is a vector function and m>1. The system can be derived from a time-dependent p-curl system which describes Bean's critical-state model in the superconductivity theory. It is shown that the degenerate system has a unique global solution. Moreover, it is shown that the weak solution is continuous and the modulus of continuity depends only on known data.