# Steady wave eq and fourier transform

1. Mar 9, 2015

### joshmccraney

1. The problem statement, all variables and given/known data
$$u_{xx} + u_{yy} = 0 : x < 0, -\infty < y < \infty$$

2. Relevant equations
We can use Fourier Transform, which is defined over some function $f(x)$ as $F(f(x)) = 1/ 2\pi \int_{-\infty}^{\infty} f(x) \exp (i \omega x) dx$.

3. The attempt at a solution
Using the fourier transform in the variable $y$ I find that $$F(u) = F(g(y)) \exp (\omega x)$$ From here I would use convolution but I don't know the inverse of $\exp (\omega x)$. Any help here (or if I should have used a fourier cosine/sine transform instead?

2. Mar 14, 2015