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Transactions of the American Mathematical Society

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Asymptotic Expansion for Layer Solutions of a Singularly Perturbed Reaction-Diffusion System

Author: Xiao-Biao Lin
Journal: Trans. Amer. Math. Soc. 348 (1996), 713-753
MSC (1991): Primary 35K57, 35B25; Secondary 34E10, 34E15
MathSciNet review: 1333395
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Abstract: For a singularly perturbed $n$-dimensional system of reaction– diffusion equations, assuming that the 0th order solutions possess boundary and internal layers and are stable in each regular and singular region, we construct matched asymptotic expansions for formal solutions in all the regular, boundary, internal and initial layers to any desired order in $\epsilon$. The formal solution shows that there is an invariant manifold of wave-front-like solutions that attracts other nearby solutions. We also give conditions for the wave-front-like solutions to converge slowly to stationary solutions on that manifold.

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Additional Information

Xiao-Biao Lin
Affiliation: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695–8205

Keywords: Asymptotic expansions, singular perturbations, reaction–diffusion systems, boundary–internal and initial layers, stability
Received by editor(s): July 5, 1994
Received by editor(s) in revised form: January 13, 1995
Additional Notes: Research partially supported by NSFgrant DMS9002803 and DMS9205535.
Article copyright: © Copyright 1996 American Mathematical Society