Non-simultaneous blow-up for a multi-coupled reaction-diffusion system

This paper deals with a reaction-diffusion system multi-coupled via inner sources and nonlinear boundary flux. The necessary and sufficient condition for the existence of non-simultaneous blow-up is proposed. Some regions of parameters are determined where both simultaneous and non-simultaneous blow-up can occur. In addition, sufficient conditions for non-simultaneous blow-up under any positive initial data are obtained.