Coupled diffusion systems with localized nonlinear reactions

This paper deals with the blowup rate and profile near the blowup time for the system of diffusion equations uit − Δui = upii+1(x0, t), (i = 1, …, k, uk+1 := u1) in Ω × (0, T) with boundary conditions ui = 0 on ∂Ω × [0, T). We show that the solution has a global blowup. The exact rate of the blowup is obtained, and we also derive the estimate of the boundary layer and on the asymptotic behavior of the solution in the boundary layer.