Approximate analytical solutions to the third-order, linear partial differential equations governing small disturbances from a uniform state in a relaxing gas are obtained. Such solutions are of interest for providing a qualitative understanding of nonequilibrium flow over thin airfoils and projectiles. Most previous investigations have, due to the complexity of the solution for even this linear problem, presented restricted results valid primarily at the flow boundaries. In contrast, the emphasis is now to provide simplified approximate expressions useful to examine properties at any point in the flow. The particular problem examined is the motion of an infinite mass of gas due to a given planar, cylindrical, or spherical piston motion. The approximation scheme used to simplify the governing equation involves the assumption that the frozen and equilibrium sound speeds are nearly equal, a condition frequently met in practice. The perturbation scheme is found to be singular due to the assumed infinite domain of the gas. The formalism of the method of matched asymptotic expansions is utilized to obtain uniformly valid solutions. Comparison of some of the approximate results is made with exact solutions determined numerically.
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