Global and Blow-Up Solutions for Nonlinear Degenerate Parabolic Systems with Crosswise-Diffusion1

In this paper the nonlinear degenerate parabolic system uts¨ a1 Uxxqau., ¨tsua2 ¨xxqb¨.with Dirichlet boundary condition is studied. The regularization method and upper]lower solutions technique are employed to show the local existence of a solution for the nonlinear degenerate parabolic system. The global existence of a solution is discussed. The finite time blow-up result together with an estimate of the blow-up time are found. The blow-up set with positive measure is analyzed in some detail.