Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



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: 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?)

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

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