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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Asymptotic Expansion for Layer Solutions of a Singularly Perturbed Reaction-Diffusion System
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by Xiao-Biao Lin PDF
Trans. Amer. Math. Soc. 348 (1996), 713-753 Request permission

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
  • Email: xblin@xblsun.math.ncsu.edu
  • 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.
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 713-753
  • MSC (1991): Primary 35K57, 35B25; Secondary 34E10, 34E15
  • DOI: https://doi.org/10.1090/S0002-9947-96-01542-5
  • MathSciNet review: 1333395