Hostname: page-component-84b7d79bbc-2l2gl Total loading time: 0 Render date: 2024-07-31T05:50:22.422Z Has data issue: false hasContentIssue false
  • English
  • Français

Hele—Shaw flow model of the injection by a point source

Published online by Cambridge University Press:  14 November 2011

Pavel Čížek  and
Vladimír Janovský
Pavel Čížek
Affiliation:
Charles University, Prague
Vladimír Janovský
Affiliation:
Charles University, Prague
Get access Rights & Permissions [Opens in a new window]

Synopsis

A variational formulation of the Hele—Shaw flow model of the point injection of fluid into a laminar cell is introduced. The analysis concerning the existence, uniqueness and regularity of a solution to the variational problem is presented.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 91 , Issue 1-2 , 1981 , pp. 147 - 159
Copyright
Copyright © Royal Society of Edinburgh 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Agmon, S., Doughs, A. and Nirenberg, L.. Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions I. Comm. Pure Appl. Math. 12 (1959), 623–727.CrossRefGoogle Scholar
2Eckeland, I. and Temam, R.. Convex Analysis and Variational Problems (Amsterdam: North Holland, 1976).Google Scholar
3Elliott, C. M. and Janovsky, V.. A variational inequality approach to Hele—Shaw flow with a moving boundary. Proc. Roy. Soc. Edinburgh Sect. A 88 (1981), 93–107.CrossRefGoogle Scholar
4Nečas, J.. Les methodés directes en théorie des équations elliptiques (Prague: Academia, 1967).Google Scholar
5Richardson, S.. Hele-Shaw flow with a free boundary produced by the injection of flow into a narrow channel. J. Fluid Mech. 56 (1972), 609–618.CrossRefGoogle Scholar
6Stampacchia, G.. Free boundary problems for Poisson's equation. North-HollandMath. Studies 21 (Amsterdam: North-Holland, 1976).Google Scholar