Would it be possible for someone to guide me through this problem.
The PDE is, $\Delta u =0$
We have the following boundary solutions: where a and b are real numbers u(0,y)=c1, u(a,y)=c1, u(x,0)=g(x), $\frac{\delta u}{\delta v}$(x,b)=c2 where c1 and c2 are real numbers.
I have to solve this for x in [0,a] and y in [0,b]
Could someone help me out for this problem. I'm beginner at PDE. I was able to break up the problem to $V^{II}=\lambda V$ and $W^{II}=-\lambda W$. I know that I have to break it up and solve 4 PDEs.
For u(0,y)=c1, and all the other boundary's zero, I found $\lambda > 0$. For u(a,y)=c1, and all the other boundary's zero, I also found $\lambda > 0$. For the last 2 solutions I found $\lambda<0$.
I think the v in $\frac{\delta u}{\delta v}$(x,b)=c2 is the outward pointing normal vector and I believe it should equal y except I can't figure out why.
I've spent hours on the problem trying to work out the solutions and I can't seem to get anywhere. Any help would be greatly appreciated!
Thank you for your time!