Differential Equations

On Gas Flow Beyond Strong Shock Wave Front, Form of Which Approaches a Certain Curve

V. I. Bogatko^a, G. A. Kolton^b, E. A. Potekhina<sup>a

a</sup> Saint-Petersburg State University
^b Saint-Petersburg State Mining Institute

Abstract: The plane auto model problem of the in viscid gas motion beyond intensive shock wave is studied. It is supposed, that shock wave front approaches some curve, the form of which is known. Solution is constructed in the form of series on the small parameter degrees. This parameter characterizes the relation of gas densities at shock wave front. Certain cases are studied as examples: when intensive shock wave front form is closely approximated to the straight line or to the circle. Solution of the problem is reduced to the Euler–Darboux equation integration.

Keywords: gas dynamics, shock wave, nonlinear equations, partial differential equations.

UDC: 533.601.1

MSC: 76L05, 35Q35

Original article submitted 29/VII/2008
revision submitted – 20/II/2009

DOI: 10.14498/vsgtu607

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