Dynamics of front solutions in a specific reaction-diffusion system in one dimension

被引：0
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作者：
Shin -Ichiro Ei
Hideo Ikeda
Takeyuki Kawana
机构：
[1] Kyushu University,Faculty of Mathematics
[2] University of Toyama,Department of Mathematics
[3] Yokohama City University,Graduate School of Integrated Science
来源：
Japan Journal of Industrial and Applied Mathematics | 2008年 / 25卷
关键词：
reaction-diffusion systems; traveling fronts; pitch-fork bifurcation; heterogeneity;
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摘要：
In this paper, two component reaction-diffusion systems with a specific bistable nonlinearity are concerned. The systems have the bifurcation structure of pitch-fork type of traveling front solutions with opposite velocities, which is rigorously proved and the ordinary differential equations describing the dynamics of such traveling front solutions are also derived explicitly. It enables us to know rigorously precise information on the dynamics of traveling front solutions. As an application of this result, the imperfection structure under small perturbations and the dynamics of traveling front solutions on heterogeneous media are discussed.
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