Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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Caustics associated with the asymptotic solution of the diffusion equation


Authors: Steven P. Anderson and Arthur D. Gorman
Journal: Quart. Appl. Math. 45 (1987), 783-787
MSC: Primary 35K55; Secondary 35C20, 58G16
DOI: https://doi.org/10.1090/qam/917026
MathSciNet review: 917026
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Abstract | References | Similar Articles | Additional Information

Abstract: The Lagrange manifold technique for finding asymptotic solutions of wave equations at turning points is adapted to diffusion-type equations.


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

  • [1] Ian N. Sneddon, Elements of partial differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1957. MR 0082600
  • [2] Jack K. Cohen and Robert M. Lewis, A ray method for the asymptotic solution of the diffusion equation, J. Inst. Math. Appl. 3 (1967), 266–290. MR 0226216
  • [3] R. Smith, Effect of non-uniform currents and depth variations upon steady discharges in shallow water, J. Fluid Mech. 110, 373-380 (1981)
  • [4] Joseph B. Keller, A geometrical theory of diffraction, Calculus of variations and its applications. Proceedings of Symposia in Applied Mathematics, Vol. 8, For the American Mathematical Society: McGraw-Hill Book Co., Inc., New York-Toronto-London, 1958, pp. 27–52. MR 0094120
  • [5] A. D. Gorman and R. Wells, A sharpening of Maslov's method of characteristics to give the full asymptotic series, Quart Appl. Math. 40 (2), 159-163 (1982)
  • [6] L. Sirovich, Techniques of asymptotic analysis, Applied Mathematical Sciences, Vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0275034
  • [7] Norman Bleistein and Richard A. Handelsman, Asymptotic expansions of integrals, 2nd ed., Dover Publications, Inc., New York, 1986. MR 863284
  • [8] Arthur D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (1985), no. 6, 1404–1407. MR 790091, https://doi.org/10.1063/1.526954

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Additional Information

DOI: https://doi.org/10.1090/qam/917026
Article copyright: © Copyright 1987 American Mathematical Society


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