Effects of boundaries on one-dimensional reaction-diffusion equations near threshold.
01 January 1985
A simple set of two reaction-diffusion equations is analyzed near the threshold for appearance of spatially periodic solutions in one dimension. Exact amplitude equations are derived to second order in the deviation from threshold. Wavevector selection is studied analytically for parameters varying slowly in space from supercritical to subcritical conditions. The nonuniversality of the selection process is demonstrated explicitly for nonpotential cases.