General Tricomi–Rassias problem and oblique derivative problem for generalized Chaplygin equations

Many authors have discussed the Tricomi problem for some second order equations of mixed type, which has important applications in gas dynamics. In particular, Bers proposed the Tricomi problem for Chaplygin equations in multiply connected domains [L. Bers, Mathematical Aspects of Subsonic and Transonic Gas Dynamics, Wiley, New York, 1958]. And Rassias proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem [J.M. Rassias, Lecture Notes on Mixed Type Partial Differential Equations, World Scientific, Singapore, 1990]. In the present paper, we discuss the general Tricomi–Rassias problem for generalized Chaplygin equations. This is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. We first give the representation of solutions of the general Tricomi–Rassias problem, and then prove the uniqueness and existence of solutions for the problem by a new method. In this paper, we shall also discuss another general oblique derivative problem for generalized Chaplygin equations.