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

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.