Sun, Ning; Liu, Weishi Flux ratios for effects of permanent charges on ionic flows with three ion species: new phenomena from a case study. (English) Zbl 07818453 J. Dyn. Differ. Equations 36, No. 1, 27-62 (2024). MSC: 34B16 37N25 92C35 PDFBibTeX XMLCite \textit{N. Sun} and \textit{W. Liu}, J. Dyn. Differ. Equations 36, No. 1, 27--62 (2024; Zbl 07818453) Full Text: DOI
Lin, Guojian Effects of ion sizes on Poisson-Nernst-Planck systems with multiple ions. (English) Zbl 07788322 Math. Methods Appl. Sci. 46, No. 11, 11842-11868 (2023). MSC: 34A26 34B16 34D15 37D10 92C35 PDFBibTeX XMLCite \textit{G. Lin}, Math. Methods Appl. Sci. 46, No. 11, 11842--11868 (2023; Zbl 07788322) Full Text: DOI
Fu, Yanggeng; Liu, Weishi; Mofidi, Hamid; Zhang, Mingji Finite ion size effects on ionic flows via Poisson-Nernst-Planck systems: higher order contributions. (English) Zbl 1519.34048 J. Dyn. Differ. Equations 35, No. 2, 1585-1609 (2023). MSC: 34C60 78A35 34B15 34E15 PDFBibTeX XMLCite \textit{Y. Fu} et al., J. Dyn. Differ. Equations 35, No. 2, 1585--1609 (2023; Zbl 1519.34048) Full Text: DOI
Chen, Jianing; Zhang, Mingji Geometric singular perturbation approach to Poisson-Nernst-Planck systems with local hard-sphere potential: studies on zero-current ionic flows with boundary layers. (English) Zbl 1505.34071 Qual. Theory Dyn. Syst. 21, No. 4, Paper No. 139, 33 p. (2022). MSC: 34C60 78A35 34E15 34B15 PDFBibTeX XMLCite \textit{J. Chen} and \textit{M. Zhang}, Qual. Theory Dyn. Syst. 21, No. 4, Paper No. 139, 33 p. (2022; Zbl 1505.34071) Full Text: DOI
Zhang, Mingji Qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes. (English) Zbl 1505.34079 Discrete Contin. Dyn. Syst., Ser. B 27, No. 12, 6989-7019 (2022). MSC: 34C60 78A35 34E15 34B15 PDFBibTeX XMLCite \textit{M. Zhang}, Discrete Contin. Dyn. Syst., Ser. B 27, No. 12, 6989--7019 (2022; Zbl 1505.34079) Full Text: DOI
Bates, Peter W.; Chen, Jianing; Zhang, Mingji Dynamics of ionic flows via Poisson-Nernst-Planck systems with local hard-sphere potentials: competition between cations. (English) Zbl 1467.92254 Math. Biosci. Eng. 17, No. 4, 3736-3766 (2020). MSC: 92E20 35Q92 PDFBibTeX XMLCite \textit{P. W. Bates} et al., Math. Biosci. Eng. 17, No. 4, 3736--3766 (2020; Zbl 1467.92254) Full Text: DOI
Aitbayev, Rakhim; Bates, Peter W.; Lu, Hong; Zhang, Lijun; Zhang, Mingji Mathematical studies of Poisson-Nernst-Planck model for membrane channels: finite ion size effects without electroneutrality boundary conditions. (English) Zbl 1420.34072 J. Comput. Appl. Math. 362, 510-527 (2019). MSC: 34C60 34B16 92C35 34E15 PDFBibTeX XMLCite \textit{R. Aitbayev} et al., J. Comput. Appl. Math. 362, 510--527 (2019; Zbl 1420.34072) Full Text: DOI
Zhang, Mingji Boundary layer effects on ionic flows via classical Poisson-Nernst-Planck systems. (English) Zbl 1397.92040 Comput. Math. Biophys. 6, No. 1, 14-27 (2018). MSC: 92C05 92C35 34A26 34B16 34D15 PDFBibTeX XMLCite \textit{M. Zhang}, Comput. Math. Biophys. 6, No. 1, 14--27 (2018; Zbl 1397.92040) Full Text: DOI
Lu, Hong; Li, Ji; Shackelford, Joseph; Vorenberg, Jeremy; Zhang, Mingji Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman’s local hard-sphere potential: analysis without electroneutrality boundary conditions. (English) Zbl 1397.34040 Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1623-1643 (2018). MSC: 34B08 34B16 37D10 92C35 34E15 34C60 PDFBibTeX XMLCite \textit{H. Lu} et al., Discrete Contin. Dyn. Syst., Ser. B 23, No. 4, 1623--1643 (2018; Zbl 1397.34040) Full Text: DOI
Eisenberg, Bob; Liu, Weishi Relative dielectric constants and selectivity ratios in open ionic channels. (English) Zbl 1394.92039 Mol. Based Math. Biol. 5, 125-137 (2017). MSC: 92C40 92C05 81V10 PDFBibTeX XMLCite \textit{B. Eisenberg} and \textit{W. Liu}, Mol. Based Math. Biol. 5, 125--137 (2017; Zbl 1394.92039) Full Text: DOI arXiv
Zhang, Mingji; Zhang, Jianbao; Acheampong, Daniel Geometric singular approach to Poisson-Nernst-Planck models with excess chemical potentials: ion size effects on individual fluxes. (English) Zbl 1394.92046 Mol. Based Math. Biol. 5, 58-77 (2017). MSC: 92C40 34A26 34B16 34D15 92C35 PDFBibTeX XMLCite \textit{M. Zhang} et al., Mol. Based Math. Biol. 5, 58--77 (2017; Zbl 1394.92046) Full Text: DOI
Di Michele, Federica; Rubino, Bruno; Sampalmieri, Rosella A steady-state mathematical model for an EOS capacitor: the effect of the size exclusion. (English) Zbl 1354.82028 Netw. Heterog. Media 11, No. 4, 603-625 (2016). MSC: 82D37 34B15 58D30 82D80 PDFBibTeX XMLCite \textit{F. Di Michele} et al., Netw. Heterog. Media 11, No. 4, 603--625 (2016; Zbl 1354.82028) Full Text: DOI
Jia, Yusheng; Liu, Weishi; Zhang, Mingji Qualitative properties of ionic flows via Poisson-Nernst-Planck systems with Bikerman’s local hard-sphere potential: ion size effects. (English) Zbl 1355.34027 Discrete Contin. Dyn. Syst., Ser. B 21, No. 6, 1775-1802 (2016). Reviewer: Robert Vrabel (Trnava) MSC: 34A26 34D15 34B15 92C35 78A37 34E20 34C45 PDFBibTeX XMLCite \textit{Y. Jia} et al., Discrete Contin. Dyn. Syst., Ser. B 21, No. 6, 1775--1802 (2016; Zbl 1355.34027) Full Text: DOI
Liu, Weishi; Tu, Xuemin; Zhang, Mingji Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. II: Numerics. (English) Zbl 1329.34104 J. Dyn. Differ. Equations 24, No. 4, 985-1004 (2012). Reviewer: Vasile Dragan (Bucureşti) MSC: 34E15 35J57 35R09 65L10 65L11 78A37 82B31 92C35 PDFBibTeX XMLCite \textit{W. Liu} et al., J. Dyn. Differ. Equations 24, No. 4, 985--1004 (2012; Zbl 1329.34104) Full Text: DOI
Ji, Shuguan; Liu, Weishi Poisson-Nernst-Planck systems for ion flow with density functional theory for hard-sphere potential: I-V relations and critical potentials. I: Analysis. (English) Zbl 1270.93011 J. Dyn. Differ. Equations 24, No. 4, 955-983 (2012). Reviewer: Vasile Dragan (Bucureşti) MSC: 34B16 34E15 35J57 35R09 78A37 82B31 92C35 PDFBibTeX XMLCite \textit{S. Ji} and \textit{W. Liu}, J. Dyn. Differ. Equations 24, No. 4, 955--983 (2012; Zbl 1270.93011) Full Text: DOI
Marinoschi, Gabriela Optimal control of metabolite transport across cell membranes driven by the membrane potential. (English) Zbl 1160.93024 Nonlinear Anal., Real World Appl. 10, No. 3, 1276-1298 (2009). MSC: 93E20 92C35 60H15 PDFBibTeX XMLCite \textit{G. Marinoschi}, Nonlinear Anal., Real World Appl. 10, No. 3, 1276--1298 (2009; Zbl 1160.93024) Full Text: DOI
Liu, Weishi One-dimensional steady-state Poisson-Nernst-Planck systems for ion channels with multiple ion species. (English) Zbl 1165.34032 J. Differ. Equations 246, No. 1, 428-451 (2009). Reviewer: Vasile Dragan (Bucureşti) MSC: 34E15 34E20 34A26 92C35 34B15 PDFBibTeX XMLCite \textit{W. Liu}, J. Differ. Equations 246, No. 1, 428--451 (2009; Zbl 1165.34032) Full Text: DOI