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

AbstractIn this paper the nonlinear degenerate parabolic system ut=vα1(Uxx+au), vt=uα2(vxx+bv) 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