摘要
This work is concerned with the stationary Poisson-Nernst-Planck equation with a large parameter which describes a huge number of ions occupying an electrolytic region. First, we focus on the model with a single specie of positive charges in one-dimensional bounded domains due to the assumption that these ions are transported in the same direction along a tubular-like mircodomain. We show that the solution asymptotically blows up in a thin region attached to the boundary and establishes the refined “near-field” and “far-field” expansions for the solutions with respect to the parameter. Moreover, we obtain the boundary concentration phenomenon of the net charge density, which mathematically confirms the physical description that the non-neutral phenomenon occurs near the charged surface. In addition, we revisit a charge-conserving Poisson-Boltzmann model for monovalent binary ions and establish a novel comparison for these two models.