# Getting around inconsistent boundary/initial conditions for coupled PDEs

I am trying to model + and - charges in a 1d box. I want to start out with uniform concentrations of both (2 in the code below) and then turn on an electric field so the charges separate to either end of the box. My boundary values are determined by setting the total (drift + diffusion) currents for each type of charge to be zero at either end of the box. Here's the code:

sol = NDSolveValue[{
D[u[t, z], {t, 1}] ==
D[u[t, z], {z, 2}] - D[u[t, z], {z, 1}], (*
charges diffuse and drift (opposite one another)*)
D[v[t, z], {t, 1}] ==
D[v[t, z], {z, 2}] + D[v[t, z], {z, 1}]  ,

(D[u[t, z], {z, 1}] /. z -> -5) - u[t, -5] == 0, (*  diff. +
drift current at boundaries is zero*)
(D[u[t, z], {z, 1}] /. z -> 5) - u[t, 5] == 0,
(D[v[t, z], {z, 1}] /. z -> -5) + v[t, -5] == 0,
(D[v[t, z], {z, 1}] /. z -> 5) + v[t, 5] == 0,

u[0, z] == 2,(*
assume uniform concentrations of charges initially*)
v[0, z] == 2
}, {u, v}, {z, -5, 5}, {t, 0, 100}] // Flatten


I am getting the NDSolveValue::ibcinc: Warning: boundary and initial conditions are inconsistent. which makes sense of course since the zero currents at the walls is inconsistent with the initial condition of uniformity.

So my quandary is how can I adjust my boundary conditions or initial conditions to give solutions that should be charge accumulations on the two ends?

My hunch is that I need to start with uniform initial conditions and then turn on the electric field; I've tried this (not shown) with HeavisideTheta[t - t_on] but the concentrations don't really change much.

N.B. I am ignoring internal electric field b/w charges.