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Given this Dirichlet problem:

$\begin{cases} \dfrac{\partial^2 u}{\partial x^2}+\dfrac{\partial^2 u}{\partial y^2}= -(\cos(x+y)+\cos(x-y)) \\ u(0,y)=\cos(y),\;\; u(\pi,y)=-\cos(y),\;\;u(x,0)=\cos(x),\;\;u\left(x,\frac{\pi}{2}\right)=0, \end{cases}$ can we apply Fourier's theory or eigenfunctions of Laplacian to express the exact solution?

(I think the answer is no, but I'm not sure why).

Thanks a lot.

  • 0
    How about show$i$ng some wor$k$??2012-12-06

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