Optimal classification for blow-up phenomena in heat equations coupled via exponential sources

This paper deals with simultaneous and non-simultaneous blow-up solutions for heat equations coupled via exponential sources, subject to null Dirichlet boundary conditions. The main results complete the previously known results on the optimal classification for simultaneous and non-simultaneous blow-up solutions by covering the whole ranges of exponents. Moreover, all kinds of simultaneous and non-simultaneous blow-up rates are obtained.