PDE:Fourier Transforms

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

There are solutions to PDEs using Fourier transforms in the Partial Differential Equations section.

1. solution Find the Fourier transform of ${\displaystyle f(t)=e^{-|t|}\,}$

2. solution Find the Fourier transform of ${\displaystyle f(t)={\begin{cases}1&|t|<1\\0&|t|>1\end{cases}}\,}$

 1. solution ${\displaystyle u_{t}=ku_{xx}\,}$ ${\displaystyle u(0,t)=0\,}$${\displaystyle u(x,0)=f(x)\,}$${\displaystyle t>0,\,\,0

 3. solution ${\displaystyle u_{t}=-u_{xxxx}\,}$ ${\displaystyle u(x,0)=f(x)\,}$${\displaystyle t>0,\,\,x\in \Re \,}$

 4. solution ${\displaystyle u_{tt}=c^{2}\,u_{xx}\,}$ ${\displaystyle u(x,0)=f(x)\,}$${\displaystyle u_{t}(x,0)=g(x)\,}$${\displaystyle t>0,\,\,x\in \Re \,}$