Publications

Preprint and Reprint

• Flux ratios for effects of permanent charges on ionic flows with three ion species: new phenomena from a case study (pdf)
  J. Dynam. Diff. Equations (with Ning Sun)
• Finite ion size effects on ionic flows via Poisson-Nernst-Planck systems: higher order contributions. (pdf)
  J. Dynam. Diff. Equations (with Y. Fu, H. Mofidi, and M. Zhang)
• Poisson-Nernst-Planck models for three ion species: Monotonic profiles vs. oscillatory profiles (pdf)
  J. Appl. Anal. Comput. 12 (2022), 1211-1233 (with L. Yan and H. Xu)
• Stationary shear flows of nematic liquid crystals: A comprehensive study via Ericksen-Leslie model. (pdf)
  J. Dynam. Diff. Equations 34 (2022), 239-269 (with J. Jiao and K. Huang).
• Permanent charge effects on ionic flow: a numerical study of flux ratios and their bifurcation. (pdf)
  Commun. Comput. Phy. 30 (2021), 486-514 (with W. Huang and Y. Yu).
• Effects of large permanent charges on ionic flows via Poisson-Nernst-Planck models. (pdf)
  SIAM J. Appl. Dyn. Syst. 19 (2020), 1993-2029 (with L. Zhang).
• Reversal potential and reversal permanent charge with unequal diffusion coefficients via classical Poisson-Nernst-Planck models. (pdf)
  SIAM J. Appl. Math. 80 (2020), 1908-1935 (with H. Mofidi).
• Effects of Diffusion Coefficients and Permanent Charges on Reversal Potentials in Ionic Channels. (pdf)
  Entropy 22 (2020), 325(1-23) (with H. Mofidi and B. Eisenberg).
• Poiseuille flow of nematic liquid crystals via the f/lil Ericksen-Leslie model. (pdf)
  Arch. Ration. Mech. Anal. 236 (2020), 839-891 (with G. Chen and T. Huang).
• An effect of large permanent charge: Decreasing flux with increasing transmembrane potential. (pdf)
  Eur.  Phys.  J.  Special Topics 227 (2019), 2575-2601 (with L. Zhang and B. Eisenberg).
• Flux ratios and channel structures. (pdf)
  J.  Dynam.  Diff.  Equations 31 (2019), 1141-1183 (with S. Ji and B. Eisenberg).
• A flux ratio and a universal property of permanent charges effects on fluxes. (pdf)
  Comput.  Math.  Biophys.  6 (2018), 28-40.
• Non-localness of excess potentials and boundary value problems of Poisson-Nernst-Planck systems for ionic flow: a case study. (pdf)
  J.  Dynam.  Diff.  Equations 30 (2018), 779-797 (with Lili Sun).
• Relative dielectric constants and selectivity ratios in open ionic channels. (pdf)
  Mol.  Based Math. Biol.  5 (2017), 125-137 (with B. Eisenberg).
• Ion size and valence effects on ionic flows via Poisson-Nernst-Planck models. Commun. (pdf)
  Math. Sci. 15 (2017), 881-901 (with Peter Bates, Hong Lu, and Mingji Zhang).
• Qualitative properties of ionic flows via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential: Ion size effects. (pdf)
  Discrete Contin. Dyn. Syst. B 21 (2016), 1775-1802 (with Yusheng Jia and Mingji Zhang).
• Turning Points and Relaxation Oscillation Cycles in Simple Epidemic Models (pdf)
  SIAM J. Appl. Math. 76 (2016), 663-687 (with M. Li, C. Shan, and Y. Yi).
• A complete analysis of a classical Poisson-Nernst-Planck model for ionic flow. (pdf)
  J. Differential Equations 258 (2015), 1192-1228 (with Hongguo Xu).
• Reversal permanent charge and reversal potential: case studies via classical Poisson-Nernst-Planck models. (pdf)
  Nonlinearity 28 (2015), 103-127 (with Bob Eisenberg and Hongguo Xu).
• Effect of (small) permanent charge and channel geometry on ionic flows via classical Poisson-Nernst-Planck models.(pdf)
  SIAM J. Appl. Math. 75 (2015), no. 1, 114-135 (with Shuguan Ji and Mingji Zhang).
• Minimizers of disclinations in nematic liquid crystals. (pdf)
• Poiseuille flow and apparent viscosity of nematic liquid-crystals. (pdf)
• Poisson-Nernst-Planck Systems for Ion Flow with a Local Hard-Sphere Potential for ion size effects. (pdf)
  SIAM J. Appl. Dyn. Syst. 12 (2013), no. 3, 1613-1648 (with G. Lin, Y. Yi, and M. Zhang).
• Linear stability of the sub-to-super inviscid transonic stationary wave for gas flow in a nozzle of varying area. (pdf)
  J. Differential Equations 254 (2013),  no. 4, 1957-1976 (with J. Hong, C.H. Hsu, and Y.C. Lin).
• Instability of low density supersonic waves of a viscous isentropic gas flow through a nozzle. (pdf)
  Fields Institute Communication Series 64 (2013), 169-183 (with M. Oh).  Authors' Note on a serious error (pdf)
• Poisson-Nernst-Planck systems for ion flow with Density Functional Theory for hard-sphere potential: I-V relations and critical potentials. Part II: Numerics. (pdf)
  J. Dynam. Differential Equations 24 (2012), no. 4, 985-1004 (with X. Tu and M. Zhang).
• Poisson-Nernst-Planck systems for ion flow with Density Functional Theory for hard-sphere potential: I-V relations and critical potentials. Part I: Analysis. (pdf)
  J. Dynam. Differential Equations 24 (2012), no. 4, 955-983 (with S. Ji).
• Steady states for shear flows of a liquid-crystal model: m/litiplicity, stability, and hysteresis. (pdf)
  J. Differential Equations 253 (2012), no. 12, 3184-3210 (with T. Dorn).
• Exponential dichotomy for asymptotically hyperbolic two-dimensional linear systems. (pdf)
  J. Dynam. Differential Equations 22 (2010), no. 4, 697-722 (with E. Van Vleck).
• Poisson-Nernst-Planck systems for narrow tub/liar-like membrane channels. (pdf)
  J. Dynam. Differential Equations 22 (2010), no. 3, 413-437 (with B. Wang).
• Viscous standing asymptotic states of isentropic compressible flows through a nozzle.
  Arch. Ration. Mech. Anal. 196 (2010), no. 2, 575-597 (with J. Hong and C.H. Hsu).
• Inviscid and viscous stationary waves of gas flow through contracting-expanding nozzles.
  J. Differential Equations 248 (2010), no. 1, 50-76 (with J. Hong and C.H. Hsu).
• One-dimensional steady-state Poisson-Nernst-Planck systems for ion channels with m/litiple ion species.
  J. Differential Equations 246 (2009), no. 1, 428-451.
• Asymptotic expansions of I-V relations via a Poisson-Nernst-Planck system.
  SIAM J. Appl. Dyn. Syst. 7 (2008), no. 4, 1507-1526 (with N. Abaid and R. S. Eisenberg).
• Asymptotic behavior of the FitzHugh-Nagumo system on the real line.
  Int. J. Evol. Equ. 2 (2007), no. 2, 129-163 (with B. Wang).
• Poisson-Nernst-Planck systems for ion channels with permanent charges.
  SIAM J. Math. Anal. 38 (2007), no. 6, 1932-1966 (with B. Eisenberg).
• Geometric sing/liar perturbation theory for problems with m/litiple turning points: invariant manifolds and exchange lemmas.
  J. Dynam. Differential Equations 18 (2006), no. 3, 667-691.
• Turning points and traveling waves in FitzHugh-Nagumo type equations.
  J. Differential Equations 225 (2006), no. 2, 381-410 (with E. Van Vleck).
• Geometric analysis of a sing/liar boundary value problem with turning points.
  Discrete Contin. Dyn. Syst. 2005, suppl., 624-633.
• Geometric sing/liar perturbation approach to steady-state Poisson-Nernst-Planck systems.
  SIAM J. Appl. Math. 65 (2005), no. 3, 754-766.
• Asymptotic phase revisited.
  J. Differential Equations 204 (2004), no. 1, 227-246 (with C. Chicone).
• M/litiple viscous wave fan profiles for Riemann solutions of hyperbolic systems of conservation laws.
  Discrete Contin. Dyn. Syst. 10 (2004), no. 4, 871-884.
• Heteroclinic foliation, global oscillations, and delay of stability loss for the Nicholson-Bailey model.
  Discrete Contin. Dyn. Syst. 9 (2003), no. 6, 1465-1492 (with S.-B. Hsu, M.-C. Li and M. Malkin).
• Relaxation oscillations in a class of predator-prey systems.
  J. Differential Equations 188 (2003), no. 1, 306-331 (with D. Xiao and Y. Yi).
• Center manifolds for general invariant sets.
  J. Differential Equations 168 (2000), no. 2, 355-385 (with S.-N. Chow and Y. Yi).
• Exchange lemmas for sing/liarly perturbed problems with certain turning points.
  J. Differential Equations 167 (2000), no. 1, 134-180.
• Invariant manifolds for a rapidly oscillatory perturbation problem.
  Differential equations and computational sim/liations (Chengdu, 1999), 215--224, World Sci. Publishing, River Edge, NJ, 2000.
• Center manifolds for smooth invariant manifolds.
  Trans. Amer. Math. Soc. 352 (2000), no. 11, 5179-5211 (with S.-N. Chow and Y. Yi).
• On the continuation of an invariant torus in a family with rapid oscillations.
  SIAM J. Math. Anal. 31 (1999/00), no. 2, 386-415 (with C. Chicone).
• Synchronization, stability and normal hyperbolicity.
  Resenhas IME-USP 3 (1997), no. 1, 139-158 (with S.-N. Chow).
• Conventional m/litipliers for homoclinic orbits.
  Nonlinearity 9 (1996), no. 1, 115-136 (with V. Afraimovich and T. Young).
• Lorenz-type attractors from codimension one bifurcation.
  J. Dynam. Differential Equations 7 (1995), no. 2, 375-407 (with V. Afraimovich and S.-N. Chow).