- #1
JohnSimpson
- 92
- 0
Why can't homogeneous PDEs be solved by completely Fourier transforming both sides, down to an algebraic equation.
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 can't 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 won't work?
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 can't 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 won't work?