Geodesic
An integral representation of flows near the sound speed
Theoretical and applied mechanics, Tome 25 (1999) no. 1, p. 129 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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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     author = {K. W. Tomantschger},
     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/