Global and blow-up solutions for non-linear degenerate parabolic systems

In this paper the degenerate parabolic system u(t)=u(alpha1)(u(xx)+av). v(t)=v(alpha2)(v(xx)+bu) with Dirichlet boundary condition is studied. For a.b <λ(1) (√ab < lambda(1) if alpha(1) not equal alpha(2)), the global existence and the asymptotic behaviour alpha(1) = alpha(2)) of solution are analysed. For a.b > lambda(1) (rootab >lambda(1) if alpha(1) not equal alpha(2)), the blow-up time, blow-up rate and blow-up set of blow-up solution are estimated and the asymptotic behaviour of solution near the blow-up time is discussed by using the 'energy' method. Copyright (C) 2003 John Wiley Sons, Ltd.