Is this integral equation solvable? If so, how?
Hello, I'm new to the forums (actually, just found you via google) and I have 2 questions (with the other I'll post in a separate thread a little later)!
My questions is this, can the following equation be solved for http://quicklatex.com/cache3/ql_ff59...52ee1b1_l3.png:
http://quicklatex.com/cache3/ql_70dc...2c8ed79_l3.png and t sufficiently large that transient/initial conditions don't matter.
We also have charge conservation:
I tried approaching this by using a Fourier transform type solution
but when I pursue this I seem to get multiple exponential integrals and things don't seem to simplify.
Any ideas? Are there additional boundary conditions I need to impose? I have almost no experience with integral equations so all suggestions welcome!