GLOBAL EXISTENCE AND BLOW-UP FOR A DEGENERATE REACTION-DIFFUSION SYSTEM WITH NONLINEAR LOCALIZED SOURCES AND NONLOCAL BOUNDARY CONDITIONS LIANG, FEI;
This paper deals with a degenerate parabolic system with coupled nonlinear localized sources subject to weighted nonlocal Dirichlet boundary conditions. We obtain the conditions for global and blow-up solutions. It is interesting to observe that the weight functions for the nonlocal Dirichlet boundary conditions play substantial roles in determining not only whether the solutions are global or blow-up, but also whether the blowing up occurs for any positive initial data or just for large ones. Moreover, we establish the precise blow-up rate.