I'm trying to solve a fourth order pde similar to the biharmonic equation
$ 0=\frac{\partial ^4}{\partial x^4}u(x,y)+Q\frac{\partial ^4}{\partial x^2 \partial y^2}u(x,y)+\frac{\partial ^4}{\partial y^4}u(x,y) $
Where Q is a constant. The boundary condition are the following,
$ \frac{\partial^2}{\partial x^2}u(x,y)=0\quad \quad \frac{\partial^2}{\partial y^2}u(x,y)=0 \quad \textit{and} \quad \frac{\partial^2}{\partial x \partial y}u(x,y)=0 $
while the boundary is a rectangle.
So far neither Fourier series nor separation of variables seems to work on this one and I'm no expert to the topic.