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A note on Kaplun limits and double asymptotics


Author: D. D. Freund
Journal: Proc. Amer. Math. Soc. 35 (1972), 464-470
MSC: Primary 41A60; Secondary 35G20
DOI: https://doi.org/10.1090/S0002-9939-1972-0303189-0
MathSciNet review: 0303189
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Abstract: The foundation of ``inner-outer'' expansions and allied methods is examined. Two limit definitions (both yielding Kaplun's extension theorem) are compared in regard to double limit asymptotics.


References [Enhancements On Off] (What's this?)

  • [1] R. E. Meyer, Near-steady transition waves of a collisionless plasma, J. Mathematical Phys. 8 (1967), 1676-1684.
  • [2] M. D. Van Dyke, Perturbation methods in fluid mechanics, Appl. Math. and Mech., vol. 8, Academic Press, New York, 1964. MR 31 #974. MR 0176702 (31:974)
  • [3] J. D. Cole, Perturbation methods in applied mathematics, Blaisdell, Waltham, Mass., 1968. MR 39 #7841. MR 0246537 (39:7841)
  • [4] Lynn M. Olson, Near-steady oblique shock waves in collisionless plasma, MRC Technical Summary Report No. 1031, University of Wisconsin, Madison, Wis., 1970.
  • [5] S. Kaplun, Fluid mechanics and singular perturbations: A collection of papers, Academic Press, New York, 1967. MR 35 #5177. MR 0214326 (35:5177)
  • [6] R. E. Meyer, On the approximation of double limits by single limits and the Kaplun extension theorem, J. Inst. Math. Appl. 3 (1967), 245-249. MR 37 #6071. MR 0230509 (37:6071)
  • [7] L. E. Fraenkel, On the method of matched asymptotic expansions. I. A matching principle, Proc. Cambridge Philos. Soc. 65 (1969), 209-231. MR 38 #6177a. MR 0237898 (38:6177a)
  • [8] M. C. Shen, Asymptotic theory of unsteady three-dimensional waves in a channel of arbitrary cross section, SIAM J. Appl. Math. 17 (1969), 260-271.

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0303189-0
Keywords: Double limit asymptotics, Kaplun limits, matched asymptotic expansions
Article copyright: © Copyright 1972 American Mathematical Society

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