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 - Funding Information:
The work was done when C.-C. Lee and T.-C. Lin were visiting the Department of Mathematics of Penn State University (PSU) during the summer of 2014. They express sincere thanks to PSU for all the hospitality and the great working environment. The authors also thank Professors Bob Eisenberg, Ping Sheng, Chiun-Chuan Chen, and Rolf Ryham for numerous interesting discussions and valuable comments. The authors also thank the anonymous referees for their helpful comments and suggestions. The research of C.-C. Lee was partially supported by the Ministry of Science and Tech-nology of Taiwan under the grants NSC-101-2115-M-134-007-MY2 andMOST-103-2115-M-134-001. Y. Hyon is partially supported by the National Institute for Mathematical Sciences grant funded by the Korean government (No. B21501). T.-C. Lin is partially supported by National Center of Theoretical Sciences (NCTS) and the Ministry of Sci-ence and Technology of Taiwan grant NSC-102-2115-M-002-015-MY4 and MOST-103-2115-M-002-005-MY3. C. Liu is partially supported by the NSF grants DMS-1109107, DMS-1216938, DMS-1159937, and DMS-1412005.
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.
UR - http://www.scopus.com/inward/record.url?scp=84957637070&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84957637070&partnerID=8YFLogxK
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 -