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 u(it)-Deltau(i) = u(i+1)(Pi) (x(0),t), (i = 1,...,k, u(k+1) := u(1)) in Omega x (0,T) with boundary conditions u(i) = 0 on partial derivative Omega x [0, T). We show that the solution has a g lobal 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 so lution in the boundary layer. (C) 2001 Elsevier Science Ltd. All rights res erved.