Abstract: This paper deals with a reaction-diffusion system with nonlocal sources. The authors first show that the solution blows up in finite time T if the initial data is large enough, then establish the estimates of the blow-up rates and the asymptotic behavior of the solution. Finally the size of the boundary layer is given.

Key words: Reaction-diffusion system, Nonlocal source, Blow-up, Blow-up rates, Boundary layer