TY - JOUR
T1 - Boundary layer solutions of charge conserving poisson-boltzmann equations
T2 - One-dimensional case
AU - Lee, Chiun Chang
AU - Lee, Hijin
AU - Hyon, Yunkyong
AU - Lin, Tai Chia
AU - Liu, Chun
N1 - Publisher Copyright:
© 2016 International Press.
PY - 2016
Y1 - 2016
N2 - For multispecies ions, we study boundary layer solutions of charge conserving Poisson-Boltzmann (CCPB) equations [L. Wan, S. Xu, M. Liao, C. Liu, and P. Sheng, Phys. Rev. X 4, 011042, 2014] (with a small parameter ε) over a finite one-dimensional (1D) spatial domain, subjected to Robin type boundary conditions with variable coefficients. Hereafter, 1D boundary layer solutions mean that as ε approaches zero, the profiles of solutions form boundary layers near boundary points and become flat in the interior domain. These solutions are related to electric double layers with many applications in biology and physics. We rigorously prove the asymptotic behaviors of 1D boundary layer solutions at interior and boundary points. The asymptotic limits of the solution values (electric potentials) at interior and boundary points with a potential gap (related to zeta potential) are uniquely determined by explicit nonlinear formulas (cannot be found in classical Poisson-Boltzmann equations) which are solvable by numerical computations.
AB - For multispecies ions, we study boundary layer solutions of charge conserving Poisson-Boltzmann (CCPB) equations [L. Wan, S. Xu, M. Liao, C. Liu, and P. Sheng, Phys. Rev. X 4, 011042, 2014] (with a small parameter ε) over a finite one-dimensional (1D) spatial domain, subjected to Robin type boundary conditions with variable coefficients. Hereafter, 1D boundary layer solutions mean that as ε approaches zero, the profiles of solutions form boundary layers near boundary points and become flat in the interior domain. These solutions are related to electric double layers with many applications in biology and physics. We rigorously prove the asymptotic behaviors of 1D boundary layer solutions at interior and boundary points. The asymptotic limits of the solution values (electric potentials) at interior and boundary points with a potential gap (related to zeta potential) are uniquely determined by explicit nonlinear formulas (cannot be found in classical Poisson-Boltzmann equations) which are solvable by numerical computations.
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U2 - 10.4310/CMS.2016.v14.n4.a2
DO - 10.4310/CMS.2016.v14.n4.a2
M3 - Article
AN - SCOPUS:84957637070
SN - 1539-6746
VL - 14
SP - 911
EP - 940
JO - Communications in Mathematical Sciences
JF - Communications in Mathematical Sciences
IS - 4
ER -