Book Review
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MathSciNet review:
3738539
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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
Alain Bensoussan, Jacques-Louis Lions, and George Papanicolaou, Asymptotic analysis for periodic structures, Studies in Mathematics and its Applications, vol. 5, North-Holland Publishing Co., Amsterdam-New York, 1978. MR 503330
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
M. Berry, Singular limits, Physics Today, 55 (2002), no. 5, 10–11.
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, DOI 10.1007/978-1-4612-0287-5
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, DOI 10.1090/S0002-9947-1983-0690039-8
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, DOI 10.1090/S0002-9947-1995-1672406-7
L. Rene 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, DOI 10.1093/imammb/dqt008
E. J. Hinch, Perturbation methods, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1991. MR 1138727, DOI 10.1017/CBO9781139172189
Mark H. Holmes, Introduction to perturbation methods, 2nd ed., Texts in Applied Mathematics, vol. 20, Springer, New York, 2013. MR 2987304, DOI 10.1007/978-1-4614-5477-9
R. L. Jerrard, Quantized vortex filaments in complex scalar fields, Proc. of the 2014 International Congress of Mathematicians, Vol III, Invited Lectures, Seoul, 2014.
J. P. Keener, Homogenization and propagation in the bistable equation, Phys. D 136 (2000), no. 1-2, 1–17. MR 1732302, DOI 10.1016/S0167-2789(99)00151-7
Joseph B. Keller, Geometrical theory of diffraction, J. Opt. Soc. Amer. 52 (1962), 116–130. MR 135064, DOI 10.1364/JOSA.52.000116
J. Kevorkian and J. D. Cole, Multiple scale and singular perturbation methods, Applied Mathematical Sciences, vol. 114, Springer-Verlag, New York, 1996. MR 1392475, DOI 10.1007/978-1-4612-3968-0
C. C. Lin and L. A. Segel, Mathematics applied to deterministic problems in the natural sciences, 2nd ed., Classics in Applied Mathematics, vol. 1, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1988. With material on elasticity by G. H. Handelman; With a foreword by Robert E. O’Malley, Jr. MR 982711, DOI 10.1137/1.9781611971347
Graeme W. Milton, The theory of composites, Cambridge Monographs on Applied and Computational Mathematics, vol. 6, Cambridge University Press, Cambridge, 2002. MR 1899805, DOI 10.1017/CBO9780511613357
James A. Murdock, Perturbations, Classics in Applied Mathematics, vol. 27, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1999. Theory and methods; Corrected reprint of the 1991 original. MR 1710387, DOI 10.1137/1.9781611971095
John C. Neu, Vortices in complex scalar fields, Phys. D 43 (1990), no. 2-3, 385–406. MR 1067918, DOI 10.1016/0167-2789(90)90143-D
John C. Neu, Vortex dynamics of the nonlinear wave equation, Phys. D 43 (1990), no. 2-3, 407–420. MR 1067919, DOI 10.1016/0167-2789(90)90144-E
John C. Neu, Singular perturbation in the physical sciences, Graduate Studies in Mathematics, vol. 167, American Mathematical Society, Providence, RI, 2015. MR 3410360, DOI 10.1090/gsm/167
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
L. Pismen, Vortices in nonlinear fields, International Series of Monographs on Physics, 100, The Clarendon Press, Oxford, 1999.
Enrique Sánchez-Palencia, Nonhomogeneous media and vibration theory, Lecture Notes in Physics, vol. 127, Springer-Verlag, Berlin-New York, 1980. MR 578345
A. Sommerfeld and J. Runge, Anwendung der Vektorrechnung auf die Grundlagen der Geometrischen Optik, Ann. Phys. 35 (1911), 277–298.
L. Tartar, The general thoery of homogenization: a personalized introduction, Lecture Notes of the Unione Matematica Italiania, 7, Springer-Verlag, Berlin, 2009.
Milton Van Dyke, Perturbation methods in fluid mechanics, Annotated edition, Parabolic Press, Stanford, Calif., 1975. MR 0416240
G. B. Whitham, Linear and nonlinear waves, Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York-London-Sydney, 1974. MR 0483954
References
- 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)
- 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
- M. Berry, Singular limits, Physics Today, 55 (2002), no. 5, 10–11.
- 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, DOI 10.1007/978-1-4612-0287-5
- 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, DOI 10.2307/1999343
- 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, DOI 10.2307/2154960
- 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, DOI 10.1093/imammb/dqt008
- E. J. Hinch, Perturbation methods, Cambridge Texts in Applied Mathematics, Cambridge University Press, Cambridge, 1991. MR 1138727, DOI 10.1017/CBO9781139172189
- Mark H. Holmes, Introduction to perturbation methods, 2nd ed., Texts in Applied Mathematics, vol. 20, Springer, New York, 2013. MR 2987304, DOI 10.1007/978-1-4614-5477-9
- R. L. Jerrard, Quantized vortex filaments in complex scalar fields, Proc. of the 2014 International Congress of Mathematicians, Vol III, Invited Lectures, Seoul, 2014.
- J. P. Keener, Homogenization and propagation in the bistable equation, Phys. D 136 (2000), no. 1-2, 1–17. MR 1732302, DOI 10.1016/S0167-2789(99)00151-7
- Joseph B. Keller, Geometrical theory of diffraction, J. Opt. Soc. Amer. 52 (1962), 116–130. MR 0135064, DOI 10.1364/JOSA.52.000116
- J. Kevorkian and J. D. Cole, Multiple scale and singular perturbation methods, Applied Mathematical Sciences, vol. 114, Springer-Verlag, New York, 1996. MR 1392475, DOI 10.1007/978-1-4612-3968-0
- 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)
- Graeme W. Milton, The theory of composites, Cambridge Monographs on Applied and Computational Mathematics, vol. 6, Cambridge University Press, Cambridge, 2002. MR 1899805, DOI 10.1017/CBO9780511613357
- 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, DOI 10.1137/1.9781611971095
- John C. Neu, Vortices in complex scalar fields, Phys. D 43 (1990), no. 2-3, 385–406. MR 1067918, DOI 10.1016/0167-2789(90)90143-D
- John C. Neu, Vortex dynamics of the nonlinear wave equation, Phys. D 43 (1990), no. 2-3, 407–420. MR 1067919, DOI 10.1016/0167-2789(90)90144-E
- John C. Neu, Singular perturbation in the physical sciences, Graduate Studies in Mathematics, vol. 167, American Mathematical Society, Providence, RI, 2015. MR 3410360
- 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
- L. Pismen, Vortices in nonlinear fields, International Series of Monographs on Physics, 100, The Clarendon Press, Oxford, 1999.
- Enrique Sánchez-Palencia, Nonhomogeneous media and vibration theory, Lecture Notes in Physics, vol. 127, Springer-Verlag, Berlin-New York, 1980. MR 578345
- A. Sommerfeld and J. Runge, Anwendung der Vektorrechnung auf die Grundlagen der Geometrischen Optik, Ann. Phys. 35 (1911), 277–298.
- L. Tartar, The general thoery of homogenization: a personalized introduction, Lecture Notes of the Unione Matematica Italiania, 7, Springer-Verlag, Berlin, 2009.
- Milton Van Dyke, Perturbation methods in fluid mechanics, Annotated edition, The Parabolic Press, Stanford, Calif., 1975. MR 0416240
- 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
DOI:
https://doi.org/10.1090/bull/1581
Published electronically:
June 15, 2017
Review copyright:
© Copyright 2017
American Mathematical Society
