- #1
Karl86
- 40
- 3
Homework Statement
I want to find the solution to the following problem:
$$\begin{cases} \nabla^2 B=c^2 B &\text{ on the half plane } x>0 \\ B=B_0 \hat{z} & \text{ for } x<0 \end{cases}$$
in the ##xz## plane. ##c, B_0 \in \mathbb{R}##
Homework Equations
I am not really sure what would be relevant. I could solve this if I knew that B is a function of only one variable
but it can a priori be a function of ##x,y,z##.
The Attempt at a Solution
I know the solution to be of the form ##C_1 e^{\frac{x}{d}} + C_2 e^{-\frac{x}{d}} ##. But I have no idea how to prove it. I have not really taken a proper course in PDEs. In particular it's not clear to me why the solution has to depend only on x, for example.
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