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  "body": "\n## Summary\n\nThe 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.\nIt is the model [[equation of mixed type|7WFKPAMQFG]]: it is [[elliptic|B4TTNHSTRX]] in the upper half-plane, [[hyperbolic|92C3S03AQZ]] in the lower half-plane, and degenerate on the $x$-axis.\nIt arises in the study of transonic flow, where the flow changes from subsonic to supersonic.\n\n## Explanations\n\n### L1 human\n\nSome equations behave like the Laplace equation in one region and like the wave equation in another.\nIn the Tricomi equation the coefficient $y$ switches sign across the $x$-axis, and the behaviour switches with it.\nAbove the axis solutions are smooth and spread information in all directions, as for a steady temperature.\nBelow the axis information travels along curves, as for waves.\nThis models air flowing around a wing, where the flow is slower than sound in one region and faster in another.\n",
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