Dynamics of Front Solutions in a Specific Reaction-Diffusion System in One Dimension
Ei, Shin-Ichiro ; Ikeda, Hideo ; Kawana, Takeyuki
Japan J. Indust. Appl. Math., Tome 25 (2008) no. 1, p. 117-147 / Harvested from Project Euclid
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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.
Publié le : 2008-02-15
Classification:  reaction-diffusion systems,  traveling fronts,  pitch-fork bifurcation,  heterogeneity 
@article{1208196868,
     author = {Ei, Shin-Ichiro and Ikeda, Hideo and Kawana, Takeyuki},
     title = {Dynamics of Front Solutions in a Specific Reaction-Diffusion System in One Dimension},
     journal = {Japan J. Indust. Appl. Math.},
     volume = {25},
     number = {1},
     year = {2008},
     pages = { 117-147},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1208196868}
}

Ei, Shin-Ichiro; Ikeda, Hideo; Kawana, Takeyuki. Dynamics of Front Solutions in a Specific Reaction-Diffusion System in One Dimension. Japan J. Indust. Appl. Math., Tome 25 (2008) no. 1, pp.  117-147. http://gdmltest.u-ga.fr/item/1208196868/