Integrable seepage equations

Well-known results of the classification of parabolic-type differential equations, possessing an infinite Lie–Bäcklund algebra, are used to describe seepage models, which, using (in general) differential substitutions, can be reduced to the heat conduction equation. Relations between the functional...

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Bibliographic Details
Published in:	Journal of applied mathematics and mechanics Vol. 76; no. 2; pp. 185 - 191
Main Authors:	Volkov, V.G., Galiakberova, L.R., Zheltova, I.S.
Format:	Journal Article
Language:	English
Published:	Elsevier Ltd 2012
Subjects:	Classification Conduction Differential equations Heat conduction Liquids Mathematical analysis Mathematical models Seepage
Online Access:	Get full text
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Summary:	Well-known results of the classification of parabolic-type differential equations, possessing an infinite Lie–Bäcklund algebra, are used to describe seepage models, which, using (in general) differential substitutions, can be reduced to the heat conduction equation. Relations between the functional parameters, characterizing the properties of the liquid and gas phases and the porous medium, are obtained that ensure the existence of such substitutions.
Bibliography:	ObjectType-Article-2 SourceType-Scholarly Journals-1 ObjectType-Feature-1 content type line 23
ISSN:	0021-8928 0021-8928
DOI:	10.1016/j.jappmathmech.2012.05.009