Ray methods for free boundary problems

Quarterly of Applied Mathematics

Volumn 64, Issue 1, 2006, Pages 41-59

  Addison, J A ^a   Howison, S D ^a   King, J R ^b  

^a UNIVERSITY OF OXFORD   (United Kingdom)

^b UNIVERSITY OF NOTTINGHAM   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY LAYERS; BOUNDARY VALUE PROBLEMS; DIFFUSION; LAPLACE TRANSFORMS; NONLINEAR EQUATIONS;

BLACK-SCHOLES PROBLEM; FREE BOUNDARY PROBLEMS; HEAT EQUATIONS; LATENT HEAT; NONLINEAR DIFFUSION EQUATIONS; RAY METHODS;

HEAT TRANSFER;

EID: 33645928715     PISSN: 0033569X     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0033-569X-06-00993-4     Document Type: Article

References (25)

1. Aronson, D.G., Gil, O., and Vazquez, J.-L. (1998). Limit behavior of focusing solutions to nonlinear diffusions. Comm. Partial Differential Equations 23 307-332. MR1608532 (98j:35082)
2. Barenblatt, G.I. (1952). On self-similar motions of a compressible fluid in a porous medium. (Russian) Akad. Nauk SSSR. Prikl. Mat. Meh. 16 419-436. MR0052948 (14:699h)
3. Chen, X., and Chadam, J. (2004). A mathematical analysis for the optimal exercise boundary of an American put option. Preprint.
4. Chevalier, E. (2004). Free boundary near the maturity of an American option on several assets. Working paper.
5. Crank, J. (1984). Free and Moving Boundary Problems. Oxford University Press. MR0776227 (87m:35225a)
6. Dewynne, J.N., Howison, S.D., Ockendon, J.R., and Xie, W. (1989). Asymptotic behaviour of solutions to the stefan problem with a kinetic condition at the free boundary. J. Austral. Math. Soc. Ser. B 31 81-96. MR1002093 (90g:80004)
7. m ∇u) as m → +∞. IMA J. Appl. Math. 37 147-154. MR0983523 (89m:76061)
8. Evans, J.D., Keller, J.B, and Kuske, R. (2002). American options with dividends near expiry. Mathematical Finance 12 219-237. MR1910594 (2003e:91079)
9. Green, G. (1837). On the motion of waves in a variable canal of small depth and width. Trans. Camb. Phil. Soc. 6.
10. Grinberg, G.A., and Chekmareva, O.M. (1971). Motion of phase interface in Stefan problems. Sov. Phys. Tech. Phys. 15 1579-1583.
11. Gurtin, M.E. (1994). Thermodynamics and the supercritical Stefan equations with nucleation. Quart. Appl. Math. 52, 133-155. MR1262324 (95a:80016)
12. Kath, W.L., and Cohen, D.S. (1982). Waiting-time behaviour in a nonlinear diffusion equation. Stud. Appl. Math. 67 79-105. MR0670736 (84a:35126)
13. King, J.R. (1993). Multidimensional singular diffusion. J. Eng. Math. 27 357-387. MR1244218 (94i:35106)
14. King, J.R. (1993). Exact multidimensional solutions to some nonlinear diffusion equations. Quart. J. Mech. Appl. Math. 46 419-436. MR1233988 (94h:35104)
15. King, J.R., Koerber, A.J., Croft, J.M., Ward, J.P., Williams, P., and Sockett, R.E. (2003). Modelling host tissue degradation by extracellular bacterial pathogens. Math. Med. Biol. 20, 227-260.
16. King, J.R., Riley, D.S., and Wallman, A.M. (1999). Two-dimensional solidification in a corner. Proc. R. Soc. Lond. A455 3449-3470. MR1807692 (2001k:80008)
17. Knessl, C. (2002). Asymptotic analysis of the American call option with dividends. Europ. J. Appl. Math. 13 587-616. MR1949725 (2003m:91082)
18. Kuske, R., and Keller, J.B. (1998). Optimal exercise boundary for an American put option. Applied Mathematical Finance 5 107-116.
19. Lacey, A.A., and Ockendon, J.R. (1985). Ill-posed free boundary problems. Control and Cybernetics 14 275-296. MR0839524 (87f:35245)
20. Lamé, G., and Clapeyron, B.P. (1831). Mémoir sur la solidification par refroidissement d'un globe liquide. Ann. Chem. Phys. 47 250-256.
21. Liouville, J. (1837). Sur le développement des fonctions on parties de fonctions en séries. J. Math. Pures Appl. 2 (1837) 16-35.
22. Sherman, B. (1971). Limiting behavior in some Stefan problems as the latent heat goes to zero. SIAM J. Appl. Math. 20 319-327. MR0293259 (45:2336)
23. Soward, A.M. (1980). A unified approach to Stefan's problem for spheres and cylinders. Proc. R. Soc. Lond. A373 131-147. MR0592750 (82c:80012)
24. Stewartson, K., and Waechter, T.T. (1976). On Stefan's problem for spheres. Proc. R. Soc. Lond. A348 415-426.
25. Wilmott, P., Howison, S.D., and Dewynne, J.N. (1995). The Mathematics of Financial Derivatives. Cambridge University Press. MR1357666 (96h:90028)