Debye layer in charge conserving Poisson-Boltzmann equation
The Poisson-Boltzmann equation is a useful equation to understand physiological interfaces, polymer science, electron interactions in a semiconductor, or more. The charge conserving Poisson-Boltzmann equation is a non-local version of the standard Poisson-Boltzmann equation, which provides us with equilibrium solutions to Poisson-Nernst-Planck equation under no flux boundary condition. In this talk we will quantitatively discuss the so-called Debye layer phenomenon in charge conserving Poisson-Boltzmann equation. Under the neutrality assumption, we provide a novel and explicit formula to evaluate the limiting electric potential inside the physical domain as a small parameter approaching to zero. In fact due to the non-local term in charge conserving Poisson-Boltzmann equation, the limiting value of electric potential inside the physical domain is not a-priorily known. Our formula reveals the crucial relationships between the limiting electric potential inside the physical domain and the Dirichlet data of the electric potential prescribed on the physical boundary. This is a joint work with Chia-Yu Hsieh.