Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Ray methods for free boundary problems

Authors: J. A. Addison, S. D. Howison and J. R. King
Journal: Quart. Appl. Math. 64 (2006), 41-59
MSC (2000): Primary 35K60, 35K65, 80M35, 41A60, 41A63
DOI: https://doi.org/10.1090/S0033-569X-06-00993-4
Published electronically: January 24, 2006
MathSciNet review: 2211377
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Abstract | References | Similar Articles | Additional Information

Abstract: We discuss the use of the WKB ansatz in a variety of parabolic problems involving a small parameter. We analyse the Stefan problem for small latent heat, the Black-Scholes problem for an American put option, and some nonlinear diffusion equations, in each case constructing an asymptotic solution by the use of ray methods.

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Additional Information

J. A. Addison
Affiliation: Mathematical Institute, 24–29 St. Giles’, Oxford, OX1 3LB, U.K.

S. D. Howison
Affiliation: Mathematical Institute, 24–29 St. Giles’, Oxford, OX1 3LB, U.K.

J. R. King
Affiliation: Theoretical Mechanics Section, University Park, Nottingham, NG7 2RD, U.K.

DOI: https://doi.org/10.1090/S0033-569X-06-00993-4
Received by editor(s): January 1, 2005
Published electronically: January 24, 2006
Additional Notes: J. A. Addison and J. R. King gratefully acknowledge financial support from the Engineering and Physical Sciences Research Council (EPSRC)
Article copyright: © Copyright 2006 Brown University

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