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Group analysis of a one-dimensional model of gas flow in a porous medium. (English. Russian original) Zbl 1440.76136

J. Appl. Math. Mech. 81, No. 4, 334-340 (2017); translation from Prikl. Mat. Mekh. 81, No. 4, 483-491 (2017).
Summary: A potential has been introduced with based on a conservation law for the simplest one-dimensional model of gas flow in a porous medium. The admissible Lie algebra of this model with this potential is extended by a new transport operator. An optimal system of non-similar subalgebras has been constructed. For one-dimensional subalgebras, all invariant submodels have been considered and the solutions have been investigated qualitatively. Group analysis can be extended by a consideration of differentially invariant submodels for subalgebras of greater dimension.

MSC:

76N15 Gas dynamics (general theory)
74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.)
76S05 Flows in porous media; filtration; seepage
17B99 Lie algebras and Lie superalgebras
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References:

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