Global existence and blowing-up of solutions to a class of coupled reaction-convection-diffusion systems

This paper concerns the global existence and blowing-up of solutions to the homogeneous Neumann problem of a coupled reaction-convection-diffusion system. The critical Fujita curve is determined and blowing-up theorem of Fujita type is established. An interesting phenomenon is that the critical Fujita curve even could be the infinite due to the convection.