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 | 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] I. N. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, New York, Chapt. 6, 1957 MR 0082600
  • [2] J. K. Cohen and R. M. Lewis, A ray method for the asymptotic solution of the diffusion equation, JIMAA 3, 266-290 (1967) 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] J. B. Keller, A geometrical theory of diffraction, in Calculus of Variations and its Applications, Proc. Symp. Appl. Math., Vol. VIII, ed. L. M. Graves, McGraw-Hill, New York, 1958 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, Springer-Verlag, New York, 1971 MR 0275034
  • [7] N. Bleistein and R. Handelsman, Asymptotic Expansions of Integrals, Dover Publications, N. Y., 1986 MR 863284
  • [8] A. D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (6), 1404-1408, 1985 MR 790091

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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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