Geodesic
An integral representation of flows near the sound speed
Theoretical and applied mechanics, Tome 25 (1999) no. 1, p. 129

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

The present paper is concerned with the Tricomi-equation \[ \etasi_{hetaheta}+si_{\eta\eta}=0 \] This differential equation of mixed type is transformed in a formal-hyperbolic equation in the complex plane. The solutions of this equation are calculated by an integral operator. For this we consider a transformation for simplifying the differential equation. The kernel of this transformation can be represented in closed form. The integral operator also provides a way for studying some properties of the solutions. This equation can be solved as well for the subsonic and supersonic zone as for their transonic line $\eta=0$ which corresponds to the sound speed. Some particular solutions of the Tricomi-equation which are already known are special cases of this solution. 
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     title = {An integral representation of flows near the sound speed},
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K. W. Tomantschger. An integral representation of flows near the sound speed. Theoretical and applied mechanics, Tome 25 (1999) no. 1, p. 129 . http://geodesic.mathdoc.fr/item/TAM_1999_25_1_a7/