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Euler-Tricomi equation

In mathematics, the Euler-Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It named for Leonard Euler and Francesco Giacomo Tricomi . .

u x x = x u y y .

It is hyperbolic in the half plane $x > 0$ and elliptic in the half plane $x < 0$ . Its characteristics are $x d x 2 = d y 2$ , which have the integral

$y\pm\frac{2}{3}x^{3/2}=C$

where $C$ is a constant of integration. The characteristics thus comprise two families of semi-cubical parabolas, with cusps on the line $x = 0$ , the curves lying on the right hand side of the y axis.

The Euler-Tricomi equation is a limiting form of Chaplygin's equation.

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10-26-2009 08:16:03
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Euler-Tricomi equation