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