Blow-up of multi-componential solutions in heat equations with exponential boundary flux

This paper deals with heat equations coupled via exponential boundary flux, where the solution is made up of $n$ components. Under certain monotone assumptions, necessary and sufficient conditions are obtained for simultaneous blow-up of at least two components for each initial datum. As for two components blowing up simultaneously, it is interesting that the representations of blow-up rates are quite different with respect to the different blow-up mechanisms and positions between the two components.