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  "body": "\n## Summary\n\nA mixed-type equation is a partial differential equation that is elliptic in one part of its domain and hyperbolic in another part.\nThe two regions are separated by a set where the equation degenerates, often a parabolic line.\nThe basic example is the [[Tricomi equation|21DD2334NR]].\nSuch equations arise in the study of transonic flow, where the speed of a gas crosses the speed of sound.\nSee the [[definition|GKFDKRHEP4]].\n\n## Explanations\n\n### L1 human\n\nThe type of a second-order equation can change from point to point when its coefficients vary.\nIn the Tricomi equation $u_{yy} + y \\, u_{xx} = 0$, the upper half plane $y \u003e 0$ is elliptic and the lower half plane $y \u003c 0$ is hyperbolic.\nSo in one region the equation behaves like the Laplace equation and in the other like the wave equation.\nFor gas flow past an airplane wing, the flow is slower than sound in one region and faster in another, and this is the physical origin of such equations.\n",
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