Bifurcation from flat-layered solutions to reaction diffusion systems in two space dimensions
Vol. 1 (1994), No. 2, Page 339--367.
Taniguchi, Masaharu
Bifurcation from flat-layered solutions to reaction diffusion systems in two space dimensions
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Abstract:
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.
Mathematics Subject Classification (1991): 35B32, 35K57, 35B25
Mathematical Reviews Number: MR1317464
Received: 1993-07-27
