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Development of singularities in some moving boundary problems

Published online by Cambridge University Press:  26 September 2008

J. R. King
J. R. King
Affiliation:
Department of Theoretical Mechanics, University of Nottingham, Nottingham NG7 2RD, UK
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Abstract

We investigate the local behaviour at the boundary singularity for the following moving boundary problems: (i) Hele-Shaw flows in which the interface is initially non-analytic; (ii) power-law Hele-Shaw flows in which the interface contains a corner; (iii) Stefan problems in which the interface contains a corner. Both well-posed (‘injection’) and ill-posed (‘suction’) problems are considered. Related results for corner development in the presence of an impermeable boundary are also noted.

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 6 , Issue 5 , October 1995 , pp. 491 - 507
Copyright
Copyright © Cambridge University Press 1995

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References

[1]Aronsson, G. & Janfalk, U. 1992 On Hele-Shaw flows for power-law fluids. Euro. J. Appl. Math. 3, 342–366.CrossRefGoogle Scholar
[2]Barenblatt, G. I. 1979 Similarity, Self-Similarity and Intermediate Asymptotics. Consultants Bureau, New York.CrossRefGoogle Scholar
[3]Crank, J. 1984 Free and Moving Boundary Problems. Clarendon Press.Google Scholar
[4]Howison, S. D. 1992 Complex variable methods in Hele-Shaw moving boundary problems. Euro. J. Appl. Math. 3, 209–224.CrossRefGoogle Scholar
[5]King, J. R., Lacey, A. A. & Vazquez, J. L. 1995 Persistence of corners in free boundaries in Hele-Shaw flow. Euro. J. Appl. Math. 6(4).CrossRefGoogle Scholar
[6]Kuiken, H. K. 1984 Etching: a two-dimensional mathematical approach. Proc. Roy. Soc. Lond. A 392, 199–225.Google Scholar
[7]Kuiken, H. K. 1985 Edge effects in crystal growth under intermediate diffusive-kinetic control. IMA J. Appl. Math. 35, 117–129.CrossRefGoogle Scholar
[8]Kuiken, H. K. 1990 Mathematical modelling of etching processes. In Free Boundary Problems: Theory and Applications, Vol. I (Hoffmann, K. H. and Sprekels, J., eds.). Longman, pp. 89–109.Google Scholar
[9]Lacey, A. A. 1983 Initial motion of the free boundary for a non-linear diffusion equation. IMA J. Appl. Math. 31, 113–119.CrossRefGoogle Scholar
[10]Ockendon, J. R. 1994. Private communication.Google Scholar
[11]Polubarinova-Kochina, P. Ya. 1962 Theory of Groundwater Movement. Princeton University Press.Google Scholar