Asymptotic characterization of stationary interfacial patterns for reaction diffusion systems
Hiromasa Suzuki · Hokkaido Mathematical Journal · 1997
We discuss asymptotic characterization of stationary interfacial patterns for reaction diffusion systems in higher dimensional spaces when the thickness of interface (denoted by\in ) tends to zero.The fact due to [14] that any stationary interfacial pattern, which has a smooth limiting configuration up to\in=0 , must become unstable for small \in implies that stable solutions must become finer and finer as \xi j \downarrow 0 .This leads to the necessity of rescaling in order to capture the limiting configuration of the stable stationary interfacial patterns.An appropriate scaling turns out to be order\in^{1/3} .The rescaled reduced equation, which determines the asymptotic profile of the interface, as well as the spectral behavior of the associated linearized eigenvalue problems are studied by using the matched asymptotic expansion method.