I consider the typical convection-diffusion equation taking into account the diffusion coefficient as a tensor like:

then, the equation will be:

In the case of the , I can solve this equation doing a change of variable and then applying the Fourier transformation. But when is a tensor, I become a partial differential equation that I cannot solve. I make the change of variable but I cannot applied the Fourier transformation because depends on .

Could some one give me other idea to solve it?