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 :

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!