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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Asymptotic phenomena in mathematical physics
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by K. O. Friedrichs PDF
Bull. Amer. Math. Soc. 61 (1955), 485-504
References
  • G. G. Stokes and G. G. Stokes, On the discontinuity of arbitrary constants that appear as multipliers of semi-convergent series, Acta Math. 26 (1902), no. 1, 393–397. A letter to the editor. MR 1554970, DOI 10.1007/BF02415503
    • G. D. Birkhoff and R. E. Langer, The boundary problems and developments associated with a system of ordinary linear differential equations of the first order, Proceedings of the American Academy of Arts and Sciences vol. 58 (1923) pp. 51-128. Reprinted in Collected mathematical papers, vol. I, pp. 347-424.[Note] M, Hukuhara, Sur les propriétés asymptotiques des solutions d’un système d’équations différentielles linéaires contenant un parametre, Kyushu Imperial University, Faculty of Engineering Memoirs, vol. 8, 1936-1940, pp. 249-280.
  • H. L. Turrittin, Asymptotic expansions of solutions of systems of ordinary linear differential equations containing a parameter, Contributions to the Theory of Nonlinear Oscillations, vol. II, Princeton University Press, Princeton, N.J., 1952, pp. 81–116. MR 0050754
    • W. Wasow, Introduction to the asymptotic theory of ordinary linear differential equations, Report of the National Bureau of Standards, 1954, pp. 54-56. M. H. Dulac, Points singuliers des equations différentielles, Memorial des Sciences Mathématique, no. 61, 1934.
  • Wolfgang Wasow, Singular perturbations of boundary value problems for nonlinear differential equations of the second order, Comm. Pure Appl. Math. 9 (1956), 93–113. MR 79161, DOI 10.1002/cpa.3160090107
    • H. S. Tsien, The PLK method, Advances in Applied Mechanics, vol. IV, Academic Press Inc., New York, 1955.
  • Wolfgang Wasow, On the convergence of an approximation method of M. J. Lighthill, J. Rational Mech. Anal. 4 (1955), 751–767. MR 73785, DOI 10.1512/iumj.1955.4.54029
  • Norman Levinson, Perturbations of discontinuous solutions of non-linear systems of differential equations, Acta Math. 82 (1950), 71–106. MR 35356, DOI 10.1007/BF02398275
  • A. B. Vasil′eva, On differential equations containing small parameters, Mat. Sbornik N.S. 31(73) (1952), 587–644 (Russian). MR 0055518
  • J. J. Stoker, Nonlinear Vibrations in Mechanical and Electrical Systems, Interscience Publishers, Inc., New York, N.Y., 1950. MR 0034932
  • Richard Bellman, Stability theory of differential equations, McGraw-Hill Book Co., Inc., New York-Toronto-London, 1953. MR 0061235
  • V. V. Nemyckiĭ, Some problems of the qualitative theory of differential equations, Uspehi Matem. Nauk (N.S.) 9 (1954), no. 3(61), 39–56 (Russian). MR 0063502
  • Norman Levinson, The first boundary value problem for $\varepsilon \Delta u+A(x,y)u_x+B(x,y)u_y+C(x,y)u=D(x,y)$ for small $\varepsilon$, Ann. of Math. (2) 51 (1950), 428–445. MR 33433, DOI 10.2307/1969333
  • P. A. Lagerstrom and J. D. Cole, Examples illustrating expansion procedures for the Navier-Stokes equations, J. Rational Mech. Anal. 4 (1955), 817–882. MR 77329, DOI 10.1512/iumj.1955.4.54032
    • R. K. Luneburg, Lecture Notes, Brown University, 1944, and New York University, 1947-1948.
  • F. G. Friedlander, Geometrical optics and Maxwell’s equations, Proc. Cambridge Philos. Soc. 43 (1947), 284–286. MR 20461, DOI 10.1017/s0305004100023483
  • F. G. Friedlander and Joseph B. Keller, Asymptotic expansions of solutions of $(\nabla ^2+k^2)u=0$, New York University, Institute of Mathematical Sciences, Division of Electromagnetic Research, 1954. Research Rep. No. EM-67. MR 0065776
    • H. Reissner, Spannungen in Kugelschalen (Kuppeln), Festschrift H. Mueller, Breslau, Leipzig, 1912, pp. 181-193. O. Blumenthal, Archiv der Mathematik und Physik (3) vol. 19 (1912) pp. 136-174.
  • Eric Reissner, A problem of finite bending of circular ring plates, Quart. Appl. Math. 10 (1952), 167–173. MR 51111, DOI 10.1090/S0033-569X-1952-51111-2
  • K. O. Friedrichs and J. J. Stoker, The non-linear boundary value problem of the buckled plate, Amer. J. Math. 63 (1941), 839–888. MR 5866, DOI 10.2307/2371625
  • E. Bromberg and J. J. Stoker, Non-linear theory of curved elastic sheets, Quart. Appl. Math. 3 (1945), 246–265. MR 13355, DOI 10.1090/S0033-569X-1945-13355-7
    • L. Prandtl, The mechanics of viscous fluids, Aerodynamic Theory, Ed. by W. F. Durand, vol. III G. (1935). S. Goldstein, Modern developments in fluid dynamics, vol. I, Oxford, 1938.
  • Walter Tollmien, Laminare Grenzschichten, Naturforschung und Medizin in Deutschland 1939–1946, Band 11, Hydro- und Aerodynamik, Verlag Chemie, Weinheim, 1953, pp. 21–53 (German). MR 0061960
  • C. C. Lin, Hydrodynamic stability, Proceedings of Symposia in Applied Mathematics, Vol. V, Wave motion and vibration theory, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1954, pp. 1–18. MR 0063199
    • J. J. Stoker, Water waves, New York, Interscience G. D. Birkhoff, Bull. Amer. Math. Soc. vol. 39 (1933) pp. 681-700.
Additional Information
  • Journal: Bull. Amer. Math. Soc. 61 (1955), 485-504
  • DOI: https://doi.org/10.1090/S0002-9904-1955-09976-2
  • MathSciNet review: 0074614