Tricomi equation

Summary

The Tricomi equation, or Euler–Tricomi equation, is the linear second-order equation $y u_{xx} + u_{yy} = 0$ for a function $u(x, y)$ in the plane. It is the model equation of mixed type: it is elliptic in the upper half-plane, hyperbolic in the lower half-plane, and degenerate on the $x$-axis. It arises in the study of transonic flow, where the flow changes from subsonic to supersonic.