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.
- Ian N. Sneddon, Elements of partial differential equations, McGraw-Hill Book Company, Inc., New York-Toronto-London, 1957. MR 0082600
- 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 226216
R. Smith, Effect of non-uniform currents and depth variations upon steady discharges in shallow water, J. Fluid Mech. 110, 373–380 (1981)
- 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
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)
- L. Sirovich, Techniques of asymptotic analysis, Applied Mathematical Sciences, vol. 2, Springer-Verlag, New York-Berlin, 1971. MR 0275034
- Norman Bleistein and Richard A. Handelsman, Asymptotic expansions of integrals, 2nd ed., Dover Publications, Inc., New York, 1986. MR 863284
- Arthur D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (1985), no. 6, 1404–1407. MR 790091, DOI https://doi.org/10.1063/1.526954
I. N. Sneddon, Elements of Partial Differential Equations, McGraw-Hill, New York, Chapt. 6, 1957
J. K. Cohen and R. M. Lewis, A ray method for the asymptotic solution of the diffusion equation, JIMAA 3, 266–290 (1967)
R. Smith, Effect of non-uniform currents and depth variations upon steady discharges in shallow water, J. Fluid Mech. 110, 373–380 (1981)
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
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)
L. Sirovich, Techniques of Asymptotic Analysis, Springer-Verlag, New York, 1971
N. Bleistein and R. Handelsman, Asymptotic Expansions of Integrals, Dover Publications, N. Y., 1986
A. D. Gorman, Vector fields near caustics, J. Math. Phys. 26 (6), 1404–1408, 1985
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Article copyright:
© Copyright 1987
American Mathematical Society
