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 . .
- uxx = xuyy.
It is hyperbolic in the half plane x > 0 and elliptic in the half plane x < 0.
Its characteristics are xdx2 = dy2, which have the integral
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.
