Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 

 

Remark on indirect matching of singularly perturbed boundary value problems


Author: Andrzej Joachim Karwowski
Journal: Quart. Appl. Math. 61 (2003), 401-433
MSC: Primary 34E05; Secondary 74B20, 74K20, 76D10
DOI: https://doi.org/10.1090/qam/1999829
MathSciNet review: MR1999829
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We examine four singularly perturbed boundary value problems. We show that it is possible to simplify the standard matching procedure by studying the boundary layer equations with the gauge function $ \eta $ as a new independent variable.


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

  • [1] Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers, McGraw-Hill Book Co., New York, 1978. International Series in Pure and Applied Mathematics. MR 538168
  • [2] Philippe G. Ciarlet, Mathematical elasticity. Vol. II, Studies in Mathematics and its Applications, vol. 27, North-Holland Publishing Co., Amsterdam, 1997. Theory of plates. MR 1477663
  • [3] Monique Dauge and Isabelle Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. I. Optimal error estimates, Asymptotic Anal. 13 (1996), no. 2, 167–197. MR 1413859
  • [4] Monique Dauge and Isabelle Gruais, Asymptotics of arbitrary order for a thin elastic clamped plate. II. Analysis of the boundary layer terms, Asymptot. Anal. 16 (1998), no. 2, 99–124. MR 1612135
  • [5] Jean Écalle, Six lectures on transseries, analysable functions and the constructive proof of Dulac’s conjecture, Bifurcations and periodic orbits of vector fields (Montreal, PQ, 1992) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 408, Kluwer Acad. Publ., Dordrecht, 1993, pp. 75–184. MR 1258519
  • [6] E. J. Hinch, Perturbation methods, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1991. MR 1138727
  • [7] Mark H. Holmes, Introduction to perturbation methods, 2nd ed., Texts in Applied Mathematics, vol. 20, Springer, New York, 2013. MR 2987304
  • [8] Andrzej J. Karwowski, Asymptotic models for a long, elastic cylinder, J. Elasticity 24 (1990), no. 1-3, 229–287. MR 1086256, https://doi.org/10.1007/BF00115560
  • [9] J. Kevorkian and J. D. Cole, Multiple scale and singular perturbation methods, Applied Mathematical Sciences, vol. 114, Springer-Verlag, New York, 1996. MR 1392475
  • [10] P. A. Lagerstrom, Matched asymptotic expansions, Applied Mathematical Sciences, vol. 76, Springer-Verlag, New York, 1988. Ideas and techniques. MR 958913
  • [11] Jens Lorenz, Nonlinear boundary value problems with turning points and properties of difference schemes, Theory and applications of singular perturbations (Oberwolfach, 1981), Lecture Notes in Math., vol. 942, Springer, Berlin-New York, 1982, pp. 150–169. MR 679352
  • [12] Ali Hasan Nayfeh, Introduction to perturbation techniques, Wiley-Interscience [John Wiley & Sons], New York, 1981. A Wiley-Interscience Publication. MR 597894
  • [13] R. E. O'Malley, ``Singular Perturbation Methods for Ordinary Differential Equations", Springer-Verlag, 1991.
  • [14] Murray H. Protter and Hans F. Weinberger, Maximum principles in differential equations, Springer-Verlag, New York, 1984. Corrected reprint of the 1967 original. MR 762825
  • [15] Milton Van Dyke, Perturbation methods in fluid mechanics, Annotated edition, The Parabolic Press, Stanford, Calif., 1975. MR 0416240
  • [16] Robert J. Walker, Algebraic curves, Springer-Verlag, New York-Heidelberg, 1978. Reprint of the 1950 edition. MR 513824

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34E05, 74B20, 74K20, 76D10

Retrieve articles in all journals with MSC: 34E05, 74B20, 74K20, 76D10


Additional Information

DOI: https://doi.org/10.1090/qam/1999829
Article copyright: © Copyright 2003 American Mathematical Society


Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2017 Brown University
Comments: qam-query@ams.org
AMS Website