Journal of the
Korean Mathematical Society JKMS

In this paper, we consider three-component reaction-diffusion system. With an integral condition and a global coupling, this system gives us an interesting free boundary problem. We shall examine the occurrence of a Hopf bifurcation and the stability of solutions as the global coupling constant varies. The main result is that a Hopf bifurcation occurs for global coupling and this motion is transferred to the stable motion for strong global coupling.

Keywords: reaction-diffusion, global coupling, free boundary problem, Hopf bifurcation

MSC numbers: 35R35, 35B32, 35B25, 35K22, 35K57