Sorry about the format, bit I have no knowledge of LateX.(adsbygoogle = window.adsbygoogle || []).push({});

A,B - are real constants

U=(U_{x},U_{y},U_{z})

I have a system of three coupled linear second order differential equations

(d_{i})^2(U_{i}) +A*Laplacian(U_{i})+ B*d_{i}[Divergence(U)]

Note: The first term is not a sum.

0<z<H, while x & y can be any real number. I have some more boundary conditions, but I feel as if I'm nowhere close to that stage.

I'm pretty stumped. I tried Fourier transforming (in x & y) and end up with a system of six coupled linear ODEs. I can find the eigenvalues (they're the roots of a cubic equation), but solving for the eigenvectors is an awful algebraic exercise. Is there anything I'm missing?

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# Puzzled by A coupled system of PDEs

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