Euler–Tricomi equation
In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named for Leonhard Euler and Francesco Giacomo Tricomi.
It is elliptic in the half plane x > 0, parabolic at x = 0 and hyperbolic in the half plane x < 0.
Its characteristics are
which have the integral
where C is a constant of integration. The characteristics thus comprise two families of semicubical parabolas, with cusps on the line x = 0, the curves lying on the right hand side of the y-axis.Particular solutions to the Euler–Tricomi equations include
where A, B, C, D are arbitrary constants.
A general expression for these solutions is:
where
The Euler–Tricomi equation is a limiting form of Chaplygin's equation.
