Stationary plane refraction problem of shock waves in the class of simple waves. Part I. General properties of the solutions

A method is used to determine the generalized solution of the stationary plane problem of refraction for weak (isentropic) shock waves. The authors formulate the boundary-value problem for a curved wall flown past by two-layer supersonic flow. One section is devoted to the determination of geometrical integrals expressing the potentials. Some general properties of the solutions and the possible forms of walls are established to ensure a solution to be obtained in the class of simple waves. The general separation principle is established, thus enabling unambigous determination of a continuous potential of generalized solution from the multivalued geometrical integrals.