Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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] Milton Van Dyke, Perturbation methods in fluid mechanics, Applied Mathematics and Mechanics, Vol. 8, Academic Press, New York-London, 1964. MR 0176702
  • [3] Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0246537
  • [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] Fluid mechanics and singular perturbations: A collection of papers by Saul Kaplun, Edited by Paco A. Lagerstrom, Louis N. Howard and Ching-shi Liu, Academic Press, New York-London, 1967. MR 0214326
  • [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 0230509
  • [7] L. E. Fraenkel, On the method of matched asymptotic expansions. I. A matching principle, Proc. Cambridge Philos. Soc. 65 (1969), 209–231. MR 0237898
    L. E. Fraenkel, On the method of matched asymptotic expansions. II. Some applications of the composite series, Proc. Cambridge Philos. Soc. 65 (1969), 233–261. MR 0237899
    L. E. Fraenkel, On the method of matched asymptotic expansions. III. Two boundary-value problems, Proc. Cambridge Philos. Soc. 65 (1969), 263–284. MR 0237900
  • [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.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 41A60, 35G20

Retrieve articles in all journals with MSC: 41A60, 35G20


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