Critical singular exponent and asymptotic estimates in the parabolic equations

This paper considers both quenching and blowup phenomena to the coupled parabolic equations with zero Dirichlet boundary. Here, one component of the solution represents the density of some chemical and the other denotes its temperature in some ignition process. All the singular phenomena have been obtained including simultaneous and nonsimultaneous blow-up or quenching, which are classified completely by the exponents. The results extend the ones in the previous paper (Liu and Chan, 2011).