Non-simultaneous versus simultaneous blow-up for coupled heat equations with positive–negative sources

This is a successive work to the previous paper [S.N. Zheng, L. Qiao, Non-simultaneous blow-up for heat equations with positive–negative sources and coupled boundary flux, Commun. Pure Appl. Anal. 6 (4) (2007), 1113–1129] of the authors. We continue considering non-simultaneous versus simultaneous blow-up for a heat equation model with positive–negative sources and coupled non-linear boundary flux. Owing to a complete classification for all the non-linear parameters of the model, we arrive at a criterion for distinguishing between non-simultaneous and simultaneous blow-up in the coupled system.