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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Conservation Laws in Group Analysis of Gas Filtration Model

Discontinuity, Nonlinearity, and Complexity 6(1) (2017) 11--17 | DOI:10.5890/DNC.2017.03.002

S.V. Khabirov

Mavlutov’s Institute of Mechanics RAS, 71 October st., Ufa, 450054, Russia

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One-dimensional gas filtration was described nonlinear parabolic equation as the conservation law. The potential of the conservation law satisfies a equation as the conservation law. The introduce of the second potential gives a system of equations which admits 6-dimensional Lie algebra. This extends group properties of initial model. With the help of optimal system of subalgebras are classified all invariant and partial invariant solutions which are reduced to invariant solutions of the initial model. Some time it is possible to find integral of invariant submodel.


This research was supported by the RFFI (14-01-97027-p-a) and the government of RF decree 220 grat 11.G34.3-1.0042.


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