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On matching principles

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Asymptotic Analysis

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 711))

Abstract

Matching principles are the key of asymptotic analysis for singular perturbation problems. Starting with some classical definitions in asymptotics we recall the principal results which have been obtained to match asymptotic expansions of a singular function; these classical results are based on Kaplun's extension theorem. After Kaplun and Fraenkel, most of the results are from W. Eckhaus; in fact, he was the first to say clearly that matching is not actually a consequence of overlapping. Following all these ideas, we discuss some theorems and rules which involve matching and try to explore some new ideas with the help of simple examples and counter-examples.

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References

  1. Kaplun, S and Lagerstrom, P.A. (1957). Asymptotic expansions of Navier-Stokes solutions for small Reynolds numbers. J. Math. and Mech., 6, 585.

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  2. van Dyke, M.D. (1964). Perturbation methods in fluid mechanics. New York-Academic Press.

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  3. Eckhaus, W. (1969). On the foundations of the method of matched asymptotic approximations. J. de Mécanique, 8, 265.

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  4. Fraenkel, L.E. (1969). On the method of matched asymptotic expansions. Part I: A matching principle. Proc. Camb. Phil. Soc., 65, 209.

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  5. Lagerstrom, P.A. and Casten, R.G. (1972). Basic concepts underlying singular perturbation Techniques. SIAM Review, 14, 63.

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  6. Eckhaus, W. (1973). Matched asymptotic expansions and singular perturbations. Amsterdam-New York, North-Holland-American Elsevier.

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  7. Mauss, J. (1974). On first order matching process for singular functions. Proceedings Scheveningen Conf. on Diff. Eq. North-Holland Math. Studies 13.

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  8. Eckhaus, W. (1977). Matching principles and composite expansions; in Singular Perturbations and Boundary Layer Theory, Brauner, Gay, Mathieu (eds.). Lecture Notes in Math. 594, Berlin, Springer Verlag.

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  9. Eckhaus, W. (1979), Asymptotic Analysis of Singular Perturbations, Amsterdam-New York, North Holland-American Elsevier.

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Authors and Affiliations

  1. Laboratoire de Mécanique U.E.R. de Mathématiques, Université Paul Sabatier, Toulouse, France

    J. Mauss

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  1. J. Mauss
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Editor information

Ferdinand Verhulst

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© 1979 Springer-Verlag

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Mauss, J. (1979). On matching principles. In: Verhulst, F. (eds) Asymptotic Analysis. Lecture Notes in Mathematics, vol 711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0062944

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  • DOI: https://doi.org/10.1007/BFb0062944

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-09245-2

  • Online ISBN: 978-3-540-35332-4

  • eBook Packages: Springer Book Archive

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