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In mathematics, the Euler-Tricomi equation is a nonlinear partial differential equation useful in the study of transonic flow. It named for Leonard Euler and Francesco Giacomo Tricomi. .
- <math>
u_{xx}=xu_{yy}.
<math>
It is hyperbolic in the half plane <math>x>0<math> and elliptic in the half plane <math>x<0<math>.
Its characteristics are <math>xdx^2=dy^2<math>, which have the integral
- <math>
y\pm\frac{2}{3}x^{3/2}=C<math>
where <math>C<math> is a constant of integration. The characteristics thus comprise two families of semi-cubical parabolas, with cusps on the line <math>x=0<math>, 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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