- #1

- 9

- 0

## Homework Statement

Use Fourier Transform in $(x_1,x_2)$ to find $u(x_1,x_2,x_3)$ when $\Delta u=0$; in $(x_1,x_2)\in \Re^2$; $x_3<0$. $\frac{\partial u}{\partial x_3}=f(x_1,x_2)$ at $x_3=0$.

(Note that $\Delta$ is the Laplace operator.)

## Homework Equations

N/A

## The Attempt at a Solution

First of all, note that this problem is not dependent on time. I believe it's because $\Delta u=0$, right? This is the first "concept" that confuses me; what kind of problem does not depend on time, and what exactly are we looking for? Am I mistaken? Does it indeed depend on time implicitly?

And the solution to be found here is $u(x_1,x_2,x_3)$, which gives heat at any point in space, regardless of time?

On the original problem (handwritten and photocopied by the professor) the $x_3<0$ was emphasized. Why?

Is it perhaps that $\Delta u=0$ only applies to $x_1$ and $x_2$, but not $x_3$?

So confused. Any advice and direction would be greatly appreciated. Thanks.