Quarterly of Applied Mathematics

Author(s): J. A. Addison; S. D. Howison; J. R. King
Journal: Quart. Appl. Math. 64 (2006), 41-59.
MSC (2000): Primary 35K60, 35K65, 80M35, 41A60, 41A63
Posted: January 24, 2006
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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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Retrieve articles in Quarterly of Applied Mathematics with MSC (2000): 35K60, 35K65, 80M35, 41A60, 41A63

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.

PII: S0033-569X-06-00993-4
Received by editor(s): January 1, 2005
Posted: 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)
Copyright of article: Copyright 2006, Brown University

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