Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.


Full text of review: PDF   This review is available free of charge.
Book Information:

Author: John Neu
Title: Singular perturbation in the physical sciences
Additional book information: Graduate Studies in Mathematics, Vol. 167, American Mathematical Society, Providence, RI, 2015, xiv+326 pp., ISBN 978-1-4704-2555-5

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

  • [1] A. Ben Soussan, J. L. Lions, and G. Papanicolaou, Asymptotic analysis of periodic structures, Studies in Mathematics and Its Applications, vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 0503330 (82h:35001)
  • [2] Carl M. Bender and Steven A. Orszag, Advanced mathematical methods for scientists and engineers, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., New York, 1978. MR 538168
  • [3] M. Berry, Singular limits, Physics Today, 55 (2002), no. 5, 10-11.
  • [4] Fabrice Bethuel, Haïm Brezis, and Frédéric Hélein, Ginzburg-Landau vortices, Progress in Nonlinear Differential Equations and their Applications, vol. 13, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1269538
  • [5] Michael G. Crandall and Pierre-Louis Lions, Viscosity solutions of Hamilton-Jacobi equations, Trans. Amer. Math. Soc. 277 (1983), no. 1, 1-42. MR 690039, https://doi.org/10.2307/1999343
  • [6] Piero de Mottoni and Michelle Schatzman, Geometrical evolution of developed interfaces, Trans. Amer. Math. Soc. 347 (1995), no. 5, 1533-1589 (English, with English and French summaries). MR 1672406, https://doi.org/10.2307/2154960
  • [7] L. R. I. Fabregas and J. Rubinstein, A mathematical model for the progression of dental caries, Math. Med. Biol. 31 (2014), no. 4, 319-337. MR 3293086, https://doi.org/10.1093/imammb/dqt008
  • [8] E. J. Hinch, Perturbation methods, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1991. MR 1138727
  • [9] Mark H. Holmes, Introduction to perturbation methods, 2nd ed., Texts in Applied Mathematics, vol. 20, Springer, New York, 2013. MR 2987304
  • [10] R. L. Jerrard, Quantized vortex filaments in complex scalar fields, Proc. of the 2014 International Congress of Mathematicians, Vol III, Invited Lectures, Seoul, 2014.
  • [11] J. P. Keener, Homogenization and propagation in the bistable equation, Phys. D 136 (2000), no. 1-2, 1-17. MR 1732302, https://doi.org/10.1016/S0167-2789(99)00151-7
  • [12] Joseph B. Keller, Geometrical theory of diffraction, J. Opt. Soc. Amer. 52 (1962), 116-130. MR 0135064, https://doi.org/10.1364/JOSA.52.000116
  • [13] J. Kevorkian and J. D. Cole, Multiple scale and singular perturbation methods, Applied Mathematical Sciences, vol. 114, Springer-Verlag, New York, 1996. MR 1392475
  • [14] C. C. Lin and L. A. Segal, Mathematics applied to deterministic problems in the natural sciences, Classics in Applied Mathematics, Vol. 1, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1988. MR 0982711 (91a:00013)
  • [15] Graeme W. Milton, The theory of composites, Cambridge Monographs on Applied and Computational Mathematics, vol. 6, Cambridge University Press, Cambridge, 2002. MR 1899805
  • [16] James A. Murdock, Perturbations: theory and methods, Classics in Applied Mathematics, vol. 27, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999. MR 1710387
  • [17] John C. Neu, Vortices in complex scalar fields, Phys. D 43 (1990), no. 2-3, 385-406. MR 1067918, https://doi.org/10.1016/0167-2789(90)90143-D
  • [18] John C. Neu, Vortex dynamics of the nonlinear wave equation, Phys. D 43 (1990), no. 2-3, 407-420. MR 1067919, https://doi.org/10.1016/0167-2789(90)90144-E
  • [19] John C. Neu, Singular perturbation in the physical sciences, Graduate Studies in Mathematics, vol. 167, American Mathematical Society, Providence, RI, 2015. MR 3410360
  • [20] Shin Ozawa, On an elaboration of M. Kac's theorem concerning eigenvalues of the Laplacian in a region with randomly distributed small obstacles, Comm. Math. Phys. 91 (1983), no. 4, 473-487. MR 727196
  • [21] L. Pismen, Vortices in nonlinear fields, International Series of Monographs on Physics, 100, The Clarendon Press, Oxford, 1999.
  • [22] Enrique Sánchez-Palencia, Nonhomogeneous media and vibration theory, Lecture Notes in Physics, vol. 127, Springer-Verlag, Berlin-New York, 1980. MR 578345
  • [23] A. Sommerfeld and J. Runge, Anwendung der Vektorrechnung auf die Grundlagen der Geometrischen Optik, Ann. Phys. 35 (1911), 277-298.
  • [24] L. Tartar, The general thoery of homogenization: a personalized introduction, Lecture Notes of the Unione Matematica Italiania, 7, Springer-Verlag, Berlin, 2009.
  • [25] Milton Van Dyke, Perturbation methods in fluid mechanics, Annotated edition, The Parabolic Press, Stanford, Calif., 1975. MR 0416240
  • [26] G. B. Whitham, Linear and nonlinear waves, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0483954

Review Information:

Reviewer: Jacob Rubinstein
Affiliation: Department of Mathematics, Technion, Israel
Email: koby@technion.ac.il
Journal: Bull. Amer. Math. Soc. 55 (2018), 123-129
MSC (2010): Primary 34E15, 34E20, 35B27, 35B40
DOI: https://doi.org/10.1090/bull/1581
Published electronically: June 15, 2017
Review copyright: © Copyright 2017 American Mathematical Society
American Mathematical Society