(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider Laplace's equation u_{xx}+ u_{yy}= 0 on the region -inf <= x <= inf, 0 <= y <= 1 subject to the boundary conditions u(x,0) = 0, u(x,1) = f(x), limit as x tends to inf of u(x,y) = 0.

Show that the solution is given by u(x,y) = F^{-1}(sinh(wy)f(hat)/sinh(wy))

2. Relevant equations

3. The attempt at a solution

I used Fourier transforms in x.

I got u(hat)(w,y) = Ae^{ky}+ Be^{-ky}

In Fourier space:

u(hat)(w,0) = F(0) = 0

u(hat)(w,1) = f(hat)(w)

But u(hat) is a function of y. My question is how do I apply the 3rd boundary condition (as this is the limit as x(not y) tends to inf) to u(hat)

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Laplace's equation

**Physics Forums | Science Articles, Homework Help, Discussion**