STABILITY OF RADIAL SOLUTIONS OF THE POISSON NERNST PLANCK SYSTEM IN ANNULAR DOMAINS

In this paper, we consider radial solutions of the Poisson-Nernst-Planck (PNP) system with variable dielectric coefficients epsilon g(x) in N-dimensional annular domains, N >= 2. When the parameter epsilon tends to zero, the PNP system admits a boundary layer solution as a steady state, which satisfies the charge conserving Poisson-Boltzmann (CCPB) equation. For the stability of the radial boundary layer solutions to the time-dependent radial PNP system, we estimate the radial solution of the perturbed problem with global electroneutrality. We generalize the argument of the one spatial dimension case (cf. [18]) and find a new way to transform the perturbed problem. By choosing a suitable weighted norm, we then derive the associated energy law which can be used to prove that the H-x(-1) norm of the solution of the perturbed problem decays exponentially in time with the exponent independent of epsilon if the coefficient of the Robin boundary condition of electrostatic potential has a suitable positive lower bound.