Hi coomast,
1. Yes, time is running from -\infty to \infty. Sorry I didn't make that clearer.
2. Unfortunately \phi(x=0, |t|<\tau) is unknown. This and the fact that \phi_x(x=0) is unknown for all time is what makes the problem hard.
Yep, it'd be great if you could find a series solution.
Hi,
I'm trying to find an analytical solution of Laplace's equation:
\phi_{xx} + \phi_{tt} = 0
with the tricky boundary conditions:
1. \phi(x=0,|t|>\tau)= 0
2. \phi(x\neq0, |t|>>\tau)=0
3. \phi_{x}(x=0, |t|<\tau)=-1
4. \phi_{t}(x, |t|>>\tau)=0
I have the following ansatz(I...