Masayasu Mimura, Shin-ichiro Ei and Masataka Kuwamura
Department of Mathematics, Hiroshima University, Hiroshima 730, Japan
(Received September 9, 1989; Accepted October 9, 1989)
Keywords: Phase Separation, Activator- Inhibitor System, Singular Perturbation
Abstract. Evolutional process of solutions is studied for some reaction-diffusion systems with activator-inhibitor kinetics
ut = e2uxx + (1 - u2)(u - z), zt = Iudx - gzin some interval I with Neumann boundary conditions. When e is very small, it is shown by using multi-time scale arguments that the dynamics of solutions is divided into three stages; The first is the occurrence of internal layers, the second is the propagation of layers with the velocity O(e) and the final is the very slow propagation of layers with the velocity O(e-A/e) for some constant A>0.