Wedge solidification with differing types of boundary conditions

IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications)

Volumn 67, Issue 6, 2002, Pages 509-524

  Hoàng, Viêt Hà ^a   Craster, R V ^b  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Conformal mapping; Fuchsian equations; Hele Shaw; Solidification

Indexed keywords

CONFORMAL MAPPING; DIFFERENTIAL EQUATIONS; PARAMETER ESTIMATION; SOLIDIFICATION;

WEDGE SOLIDIFICATION;

BOUNDARY CONDITIONS;

EID: 0036895549     PISSN: 02724960     EISSN: None     Source Type: Journal    
DOI: 10.1093/imamat/67.6.509     Document Type: Article

References (18)

1. Abramowitz, M. & Stegun, I.A. (1969) Handbook of Mathematical Functions. New York: Dover.
2. Bakker, M. (1996) Groundwater flow with free boundaries using the hodograph method. Adv. Water Res. 20, 207-216.
3. Craster, R.V. (1994) Two related free boundary problems. IMA J. Appl. Math. 52, 253-270.
4. Craster, R.V. (1997) The solution of a class of free boundary problems. Proc. R. Soc. A 453, 607-630.
5. Craster, R.V. & Hoàng, V.H. (1998) Applications of Fuchsian differential equations to free boundary problems. Proc. R. Soc. A 454, 1241-1252.
6. Cummings, L.J. (1999) Flow around a wedge of arbitrary angle in a Hele-Shaw cell. European Journal of Applied Mathematics 10, 547-560.
7. Detournay, C. & Strack, O.D.L. (1988) A new approximate technique for the hodograph method in groundwater flow and its application to coastal aquifers. Water Resour. Res. 24, 1471-1481.
8. Erdélyi, A., Magnus, W., Oberhettinger, F. & TRICOMI, F.G. (1953) Higher Transcendental Functions, Vols I,II, III. New York: MCGraw-Hill.
9. Hoàng, H.V., Hill, J.M. & Dewynne, J.N. (1998) Pseudo steady-state solutions for solidification in a wedge. IMA J. Appl. Math. 60, 109-121.
10. Howison, S.D. & King, J.R. (1989) Explicit solutions to six free-boundary problems in fluid flow and diffusion. IMA J. Appl. Math 42, 155-175.
11. Ince, E.L. (1927) Ordinary Differential Equations. London: Longman.
12. King, J.R., Riley, D.S. & Wallman, A.M. (1999) Two-dimensional solidification in a corner. Proc. R. Soc. A 455, 3449-3470.
13. Nehari, Z. (1952) Conformal Mapping. New York: MCGraw-Hill.
14. Polubarinova-Kochina, P.Y. (1939a) An application of the theory of linear differential equations to some problems of groundwater motion (number of singular points greater than three). Izv. Akad. Nauk SSSR 5, 579-602.
15. Polubarinova-Kochina, P.Y. (1939b) An application of the theory of linear differential equations to some problems of groundwater motion (three singular points). Izv. Akad. Nauk SSSR 3, 329-350.
16. Ronveaux, A. (1995) Heun's Differential Equations. Oxford: Oxford University Press.
17. Shanin, A.V. & Craster, R.V. (2002) Removing false singular points as a method of solving ordinary differential equations, to appear.
18. Whittaker, E.T. & Watson, G.N. (1927) A Course of Modern Analysis. Cambridge: Cambridge University Press.