Exact solution of an automodel (self-sustaining) problem regarding the motion of a nonviscous heat-conducting gas bounded by a vacuum

The one-dimensional transient motion of a nonviscous, compressible, heat-conducting, gas bordered on one side by free space and on the other by a solid wall is considered. The boundary conditions at the wall are taken in a form which ensures an automodel (self-sustaining) state. An exact solution is obtained for the problem, and this is then compared with a numerical calculation.