Geodesic
Mathematical model of the gas flow in the shock front
Eurasian mathematical journal, Tome 4 (2013) no. 3, pp. 132-136.

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In this paper, an approximate solution of the problem of the structure of shock waves in gases is presented. Changes of the average magnitude of density, speed and internal energy of gas along with the width of the shock wave are given. Dependence of the width of the jump on the Mach number is obtained and is compared with results of other authors. 
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S. K. Matveev; N. Zh. Jaichibekov. Mathematical model of the gas flow in the shock front. Eurasian mathematical journal, Tome 4 (2013) no. 3, pp. 132-136. http://geodesic.mathdoc.fr/item/EMJ_2013_4_3_a11/

[1] S. K. Matveev, G. V. Kocheryzhenkov, “The structure of shock waves in gases and gas suspensions”, Dynamic processes in gases and solids, Leningrad, 1990, 28–36

[2] N. Zh. Jaichibekov, S. K. Matveev, “An application of a three-component model to the calculation of flow around bodies by gas suspension and rarefied gas”, Journal of Applied Mechanics and Technical Physics, Academy of Sciences of USSR, 1991, no. 1, 39–42

[3] S. K. Matveev, N. Zh. Jaichibekov, “Calculation of flow around a sphere by rarefied gas with an arbitrary Knudsen number”, Bulletin of the St. Petersburg University. Ser. 1, 1992, no. 2(8), 77–81 | Zbl

[4] S. K. Matveev, “Mathematical description of the flow of gas suspension arond bodies taking into account the effects of reflected particles”, The motion of compressible fluids and heterogeneous environments, Leningrad, 1982, 189–201