On electro-kinetic fluids: one-dimensional configurations (Q2493502)

The authors examine qualitative properties of solutions to a Poisson-Boltzmann equation when the Debye constant \(\varepsilon\) approaches zero. In particular, they prove that the solution are covcave and converge uniformly to a constant in the interior. The boundary layer has an \(\varepsilon\) thickness, and the limiting profile is exponential. Some properties can be generalized to higher dimensions. The proof is based on a modified Galerkin method and energy laws. The authors also present some results of numerical simulation.