In mathematics, the Euler–Tricomi equation is a linear partial differential equation useful in the study of transonic flow. It is named after mathematicians 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
A general expression for particular solutions to the Euler–Tricomi equations is:
where
These can be linearly combined to form further solutions such as:
for k = 0:
for k = 1:
etc.
The Euler–Tricomi equation is a limiting form of Chaplygin's equation.
See also Burgers' equation Chaplygin's equation List of topics named after Leonhard Euler
Bibliography A. D. Polyanin, Handbook of Linear Partial Differential Equations for Engineers and Scientists, Chapman & Hall/CRC Press, 2002.
External links Tricomi and Generalized Tricomi Equations at EqWorld: The World of Mathematical Equations.