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A free surface problem arising in the drainage of a uniformly irrigated field: Existence and uniqueness results

Part of: Miscellaneous topics - Partial differential equations

Published online by Cambridge University Press:  09 April 2009

John Van Der Hoek ,
C. J. Barnes  and
J. H. Knight
John Van Der Hoek
Affiliation:
Department of Pure Mathematics, University of AdelaideAdelaide, S. A. 5000, Australia
C. J. Barnes
Affiliation:
CSIRO Division of Soils Waite Road Urbrae, S. A. 5064, Australia
J. H. Knight
Affiliation:
CSIRO Division of Mathematics and Statistics PO Box 218 Linfield, N.S.W. 2070, Australia
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Abstract

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A field comprising uniformly porous soil overlying an impervious subsoil is drained through equally spaced tile drains placed on the boundary between the two layers of soil. When this field is subject to uniform irrigation, a free boundary forms in the porous region above the zone of saturation. We study the free boundary value problem which thus arises using the theory of variational inequalities. Existence and uniqueness results are established.

MSC classification

Secondary: 35R35: Free boundary problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 36 , Issue 3 , June 1984 , pp. 389 - 403
Copyright
Copyright © Australian Mathematical Society 1984

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