Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-02T18:47:42.216Z Has data issue: false hasContentIssue false
  • English
  • Français

An elliptic-parabolic free boundary problem: continuity of the interface

Published online by Cambridge University Press:  14 November 2011

J. Hulshof
J. Hulshof
Affiliation:
Mathematisch Instituut, Rÿksuniversiteit Leiden, Postbus 9512, 2300 RA Leiden, The Netherlands
Get access Rights & Permissions [Opens in a new window]

Synopsis

In this paper we establish continuity of the interface of the weak solution to an elliptic-parabolic problem. The physical background is the theory of partially saturated fluid flows in porous media. Our method is based on the maximum principle for parabolic equations. An essential assumption is that the flow is one-dimensional.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 106 , Issue 3-4 , 1987 , pp. 327 - 339
Copyright
Copyright © Royal Society of Edinburgh 1987

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

1Lianzun, An. Some properties of the solution of filtration problem in partially saturated porous media (Report, Tsinghua University, Beijing, 1984).Google Scholar
2Bear, J.. Dynamics of fluids in porous media (New York: Elsevier, 1972).Google Scholar
3Duyn, C. J. van. Nonstationary filtration in partially saturated media: continuity of the free boundary. Arch. Rational Mech. Anal. 79 (1982), 261–265.Google Scholar
4Duyn, C. J. van and Peletier, L. A.. Nonstationary filtration in partially saturated porous media. Arch. Rational Mech. Anal. 78 (1982), 173–198.CrossRefGoogle Scholar
5Bertsch, M. and Hulshof, J.. Regularity results for an elliptic-parabolic free boundary problem. Trans. Amer. Math. Soc. 297 (1986), 337–350.CrossRefGoogle Scholar
6Hulshof, J.. Bounded weak solutions of an elliptic-parabolic Neumann problem. Trans. Amer. Math. Soc. (to appear).Google Scholar
7Hulshof, J. and Peletier, L. A.. An elliptic-parabolic free boundary problem. J. Nonlinear Anal. 10 (1986), 1327–1346.CrossRefGoogle Scholar
8Kroner, D.. Parabolic regularization and behaviour of the free boundary for unsaturated flow in a porous medium. J. Reine Angew. Math. 348 (1984), 180–196.Google Scholar
9Matano, H.. Nonincrease of the lapnumber of a solution for a one-dimensional semilinear parabolic equation. Pub. Fac. Sci. Univ. Tokyo, Sect. 1A29 (1982), 401–441.Google Scholar
10Sabinina, E. S.. On a class of nonlinear degenerating parabolic equations, Dokl. Akad. Nauk SSSR 143 (1962), 794–797; Soviet Math. Dokl. 3 (1962), 495–498.Google Scholar
11Ning, Su and Jiunguo, Li. The boundary value problems for the filtration equation in partially saturated porous media (Report, Tsinghua University, Beijing 1984).Google Scholar
12Duyn, C. J. van and Hulshof, J.. An elliptic-parabolic problem with a nonlocal boundary condition. Arch. Rational Mech. Anal, (to appear).Google Scholar