The behavior of small perturbations of one-dimensional stationary transonic flows

The paper examines the behavior of nonstationary perturbations of stationary solutions of quasi-linear hyperbolic or parabolic degenerate systems of differential equations in the neighborhood of a critical point, defined as a point at which one of the characteristic velocities of the system becomes zero. The unknown functions of these equations are considered to depend on two functions, the coordinate x and time t, while the number of unknown functions is considered to be arbitrary. In gas dynamics, the presence of critical points of the type studied indicates the occurrence of transonic flow.