  The dynamics of ionization fronts that generate a conducting body, are in
simplest approximation equivalent to viscous fingering without regularization.
Going beyond this approximation, we suggest that ionization fronts can be
modeled by a mixed Dirichlet-Neumann boundary condition. We derive exact
uniformly propagating solutions of this problem in 2D and construct a single
partial differential equation governing small perturbations of these solutions.
For some parameter value, this equation can be solved analytically which shows
that the uniformly propagating solution is linearly convectively stable.
