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Analysis of the Stationary Filtration Problem with a Multivalued Law in the Presence of a Point Source

Analysis of the Stationary Filtration Problem with a Multivalued Law in the Presence of a Point... Differential Equations, Vol. 41, No. 7, 2005, pp. 915–922. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 7, 2005, pp. 874–880. Original Russian Text Copyright c 2005 by Badriev, Zadvornov. PARTIAL DIFFERENTIAL EQUATIONS Analysis of the Stationary Filtration Problem with a Multivalued Law in the Presence of a Point Source I. B. Badriev and O. A. Zadvornov Kazan State University, Kazan, Russia Received March 1, 2005 INTRODUCTION The present paper deals with the analysis of a mathematical model of a nonlinear stationary ltration problem for an incompressible uid governed by a multivalued ltration law with a limit gradient (e.g., see [1]) in an arbitrary bounded domain with a point source. We assume that the function determining the ltration law has a linear growth at in nity. For a special form of the domain, this problem has a solution (e.g., see [2, 3]). In the case of an arbitrary bounded domain, it was proved in [4{6] that there exists a generalized solution of the problem with ltration law given by a function of power-law (in particular, linear) growth at in nity. The generalized problem is stated there as a variational inequality with an operator that, (1) in the case of linear http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Analysis of the Stationary Filtration Problem with a Multivalued Law in the Presence of a Point Source

Differential Equations , Volume 41 (7) – Sep 30, 2005

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References (2)

Publisher
Springer Journals
Copyright
Copyright © 2005 by MAIK "Nauka/Interperiodica"
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1007/s10625-005-0231-1
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 41, No. 7, 2005, pp. 915–922. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 7, 2005, pp. 874–880. Original Russian Text Copyright c 2005 by Badriev, Zadvornov. PARTIAL DIFFERENTIAL EQUATIONS Analysis of the Stationary Filtration Problem with a Multivalued Law in the Presence of a Point Source I. B. Badriev and O. A. Zadvornov Kazan State University, Kazan, Russia Received March 1, 2005 INTRODUCTION The present paper deals with the analysis of a mathematical model of a nonlinear stationary ltration problem for an incompressible uid governed by a multivalued ltration law with a limit gradient (e.g., see [1]) in an arbitrary bounded domain with a point source. We assume that the function determining the ltration law has a linear growth at in nity. For a special form of the domain, this problem has a solution (e.g., see [2, 3]). In the case of an arbitrary bounded domain, it was proved in [4{6] that there exists a generalized solution of the problem with ltration law given by a function of power-law (in particular, linear) growth at in nity. The generalized problem is stated there as a variational inequality with an operator that, (1) in the case of linear

Journal

Differential EquationsSpringer Journals

Published: Sep 30, 2005

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