Blowup and global existence of solutions for a catalytic converter in interphase heat-transfer

In this paper we investigate the blowup property and global existence of a solution for a coupled system of first-order partial differential equation and ordinary differential equation which arises from a catalytic converter in automobile engineering. It is shown, in terms of a single physical parameter σ, that a unique bounded global solution exists if σ < under(σ, {combining low line}) and the solution blows up in finite time if σ > over(σ, -), where under(σ, {combining low line}) < over(σ, -). Various estimates for over(σ, -) and its associate blow-up time T^* are explicitly given. The value of T^* can be used to estimate the ignition time and ignition length of the ignition system which is an important concern in automobile engineering.