FINITE-TIME BLOW-UP FOR COUPLED NONLINEAR PARABOLIC SYSTEMS WITH MIXED NONLINEAR BOUNDARY CONDITIONS

This paper deals with the analysis of finite-time blow-up for a class of coupled nonlinear parabolic systems subject to mixed nonlinear boundary conditions. Under suitable assumptions, we establish a sufficient criterion ensuring finite-time blow-up of positive solutions and derive an explicit upper estimate for the blow-up time. Furthermore, a finite-difference semidiscretization of the coupled problem is used to investigate the corresponding numerical blow-up behavior. By choosing some initial data, we obtain the numerical blow-up time when the mesh size tends to zero. Finally, several numerical experiments are presented to illustrate our result.