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The Tricomi equation yuxx+uyy = 0 is a simple and useful PDE that captures the key...

The Tricomi equation yuxx+uyy = 0 is a simple and useful PDE that captures the key characterisitics of transonic flow, where the supersonic and subsonic flows are present in flow field simultaneously.

  1. (a) Show that the Tricomi equation is of mixed type. Identify the regions on the x−y plane where the PDE becomes elliptic, parabolic, and hyperbolic.

  2. (b) Assuming u(0, y) = u(L, y) = 0, obtain the Airy equation G′′(y) − k2yG(y) = 0 from the Tricomi equation by separation of variables. Note, you are not required to solve this equation.

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