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General Tricomi-Rassias problem and oblique derivative problem for generalized Chaplygin equations. (English) Zbl 1130.35096

The Tricomi problem for some second-order equations of mixed type, which has important applications in gas dynamics, is discussed from many authors. In particular, [L. Bers, Mathematical aspects of subsonic and transonic gas dynamics, Wiley: New York, (1958; Zbl 0083.20501)] proposed the Tricomi problem for Chaplygin equations in multiply connected domains. [J. M. Rassias, Lecture notes on mixed type partial differential equations, World Scientific: Singapore (1990; Zbl 0947.35504)] proposed the exterior Tricomi problem for mixed equations in a doubly connected domain and proved the uniqueness of solutions for the problem. Here the general Tricomi-Rassias problem for generalized Chaplygin equations is under discussion – this is one general oblique derivative problem that includes the exterior Tricomi problem as a special case. The representation of solutions of the general Tricomi-Rassias problem is given for the first time, and the uniqueness and existence of solutions for the problem are proved by a new method. It is also discussed another general oblique derivative problem for generalized Chaplygin equations.

MSC:

35M10 PDEs of mixed type
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