Tohoku Mathematical Journal · 1990 · 39 citations · 11 references
Natural SciencesMathematicsDifferential EquationsDynamical SystemsPattern FormationPartial Differential EquationsPerturbation MethodsPerturbation TheoryReaction-diffusion SystemsSingular Perturbation TheoryStability TheoryCoupled Reaction-diffusion EquationsReaction - Diffusion KineticsReaction - Diffusion ModelingReaction-diffusion EquationsReaction-diffusion PhenomenaReaction-diffusion-advection ModelsSingular Perturbation AnalysisSpatial Pattern Formation
In mathematical biology, reaction-diffusion equations have been of great interest as a model describing spatial pattern formations. One of the most powerful approaches to the existence of spatially inhomogeneous solutions is a singular perturbation method. In fact, this method enables us to construct solutions with sharp spatial transition layers [5], [6], [12], It is the purpose of this paper to present a method to construct solutions with internal transition layers in the context of singular perturbation problems. We also emphasize the stability analysis of the solutions so obtained as above. Our method is slightly different from those in [5], [6], [12],
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