Mathematical Aspects of Subsonic and Transonic Gas Dynamics by Lipman Bers

Author:Lipman Bers [Lipman Bers]
Language: eng
Format: epub
Publisher: Dover Publications, Inc
Published: 2016-03-14T16:00:00+00:00

Vincenti and Wagoner [345] showed that the relation can be also written in the form

Here k1 and k2 are numerical constants.

17.UNIQUENESS THEOREMS FOR EQUATIONS OF MIXED TYPE

Tricomi problem

Tricomi was the first to pose a correctly set boundary value problem for an equation of mixed type and a domain intersected by the parabolic line. He showed that (16.1) has a unique solution defined in a domain bounded by a curve in y > 0 and two characteristics Γ1, Γ2 (Fig. 17.1); this solution assumes prescribed boundary values on the elliptic boundary and on one of the two characteristics. The same “Tricomi problem” was considered by Gellerstedt [127], [128] for (16.17). We shall consider all boundary value problems for the more general equation (16.2).

Gellerstedt also observed that one can consider a more general domain bounded by and by several characteristics. In the domain shown in Fig. 17.2, the boundary values are prescribed on and on the two characteristics BD and OC. Further generalizations have been suggested by Halilov [158], [159], Bitsadze [47], Karmanov [195], and others. We mention one example only. The domain is shown on Fig. 17.3; it is multiply connected; boundary values are given on the whole elliptic boundary and on the characteristics BC, DE, GH.

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