Is it possible to solve the Poisson's equation with the Fourier transform?
Let \begin{align} -\partial_x^2 u(x)=f(x),\quad x\in\mathbb{R} \end{align} then $u(x)=\mathcal{F}^{-1}\left( \frac{1}{\xi^2}\widehat{f}(\xi)\right)$?
Asked
Active
Viewed 61 times
0
-
If $u$ is defined on the whole real line with suitable boundary conditions at infinity then probably. The domain and boundary conditions are crucial to the solution process though. On a finite interval Fourier series come into play and on the half line Laplace transform – Paul Jul 09 '23 at 22:32