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 σσ, that a unique bounded global solution exists if σ<σ̲ and the solution blows up in finite time if σ>σ¯, where σ̲<σ¯. Various estimates for σ¯ and its associate blow-up time T*T* are explicitly given. The value of T*T* can be used to estimate the ignition time and ignition length of the ignition system which is an important concern in automobile engineering.