Why can't homogeneous PDEs be solved by completely fourier transforming both sides, down to an algebraic equation.(adsbygoogle = window.adsbygoogle || []).push({});

To clarify, consider the diffusion equation Del-Squared u = du/dt

If we fourier transform both sides with respect to all 3 spatial variables and the time variable, we have something along the lines of

k^2 U = omega*U

which I cant seem to do anything useful with. What am I missing, or, if I'm not missing anything, is there a deeper reason behind why this approach wont work?

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# Fourier Transforms

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