Bifurcation from flat-layered solutions to reaction diffusion systems in two space dimensions
Masaharu Taniguchi · Institutional Repositories DataBase (IRDB) · 1994
Bifurcation from equilibrium solutions to reaction diffusion systems is considered in a two-dimensional domain. This solution has an internal transition layer that forms a flat interface. If the length of the interface in the tangential direction is small enough, the equilibrium solution is stable, but it is unstable if the length is larger than some critical value. In this paper, it is shown that bifurcation occurs at this critical length. We construct the bifurcating solutions and discuss their stability. Numerical results suggest that the bifurcation is subcritical.