Discontinuity, Nonlinearity, and Complexity
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
Download Full Text PDF
Abstract
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.
Acknowledgments
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.
References
-
| [1] | Barenblut, G.I., Entov, V.M., and Rizhik, V.M. (1972), Theory of unstable filtration of fluid and gas, Nedra: Moscow. |
-
| [2] | Ovsiannikov, L.V. (1978), Group Analysis of Differential Equations, Nauka: Moscow, (English translation, Ames, W.F.(ed.), Academic Press: New York, 1982). |
-
| [3] | Chirkunov, Yu.A., Khabirov, S.V. (2012), Elements of symmetry analysis of differential equations of continuum mechanics, NGTU: Novosibirsk. |
-
| [4] | Khabirov, S.V. (2013), A hierarchy of submodels of differential equations, Siberian Mathematical Journal, 54(6), 1111-1120. |
