PUBLICATIONS | mingji-zhang

SELECTED PUBLICATIONS AND PREPRINTS

PART I: ION CHANNEL PROBLEMS & POISSON-NERNST-PLANCK MODEL

[1] W. Liu, X. Tu and M. Zhang, Poisson-Nernst-Planck type models for ionic flow with hard sphere ion species: I-V relations and critical potentials. Part II: Numerics. Journal of Dynamics and Differential Equations, 24 (4) (2012), 985-1004.

[2] G. Lin, W. Liu, Y. Yi and M. Zhang, Poisson-Nernst-Planck systems for ion flow with density functional theory for local hard-sphere potential. SIAM Journal on Applied Dynamical Systems, 12 (3) (2013), 1613-1648.

[3] S. Ji, W. liu and M. Zhang, Effects of (small) permanent charges and channel geometry on ionic flows via classical Poisson-Nernst-Planck models. SIAM Journal on Applied Mathematics, 75(1) (2015), 114-135 (PDF).

[4] P. W. Bates, Y. Jia, G. Lin, H. Lu and M. Zhang, Individual flux study via steady-state Poisson-Nernst-Planck systems: Effects from Boundary conditions. SIAM Journal on Applied Dynamical Systems, 16(1) (2017), 410-430.

[5] Z. Wen, L. Zhang and M. Zhang, Dynamics of classical Poisson-Nernst-Planck systems with multiple cations and boundary layers. Journal of Dynamics and Differential Equations, 33 (2021), 211-234.

[6] J. Chen, Y. Wang, L. Zhang and M. Zhang, Mathematical analysis of Poisson-Nernst-Planck models with permanent charges and boundary layers: Studies on individual fluxes. Nonlinearity, 34 (2021), 3879-3906. AAM PDF

[7] P. W. Bates, Z. Wen and M. Zhang, Small permanent charge effects on individual fluxes via via classical Poisson-Nernst-Planck systems with multiple cations. Journal of Nonlinear Science, 31 (2021), 1-62. DOI: 10.1007/s00332-021-09715-3 PDF

[8] Z. Wen, P. W. Bates and M. Zhang, Effects on I-V relations from small permanent charge and channel geometry via classical Poisson-Nernst-Planck equations with multiple cations. Nonlinearity, 34 (2021), 4464-4502. AAM PDF

[9] J. Chen and M. Zhang, Geometric singular perturbation approach to Poisson-Nernst-Planck systems with local hard-sphere potential: Studies on zero-current ionic flows with boundary layers. Qualitative Theory of Dynamical Systems, (2022) 21: 139.

[10] M. Zhang, Qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes. Discrete and Continuous Dynamical Systems Series B, 27(12) (2022), 6989-7019.

[11]Y. Fu, W. Liu, H. Mofidi and M. Zhang, Finite ion size effects on ionic flows via Poisson-Nernst-Planck systems: Higher order contributions. Journal of Dynamics and Differential Equations, 35 (2023), 1585-1609.

[12] H. Mofidi, F. Hadadifard and M. Zhang, Analysis of critical transitions in flux ratios in ionic flows via classical Poisson-Nernst-Planck models. Studies in Applied Mathematics (2025), 155(2), e70087

[13] Y. Wang, J. Shen, L. Zhang and M. Zhang, Studies on reversal potential via classical Poisson-Nernst-Planck systems. Part I: Multiple pieces of nonzero permanent charges having the same sign. Qualitative Theory of Dynamical Systems (to appear).

PART II: NONLINEAR PARTIAL DIFFERENTIAL EQUATIONS

[1] H. Lu, P. W. Bates, S. Lv and M. Zhang, Dynamics of 3D fractional complex Ginzburg-Landau equation.

Journal of Differential Equations, 259 (2015), 5276-5301.

[2] H. Lu, P. W. Bates, J. Xin and M. Zhang, Asymptotic behavior of stochastic fractional power dissipative equations on R^n. Nonlinear Analysis TMA, 128 (2015), 176-198.

[3] H. Lu, S. Lv and M. Zhang, Fourier spectral approximation to the dynamical behavior of 3D fractional

Ginzburg-Landau equation. Discrete and Continuous Dynamical Systems Series A, 37(5) (2017), 2539-2564.

[4] H. Lu, P. W. Bates, W. Chen and M. Zhang, The spectral collocation method for efficiently solving PDEs with fractional Laplacian. Advances in Computational Mathematics, 44(3) (2018), 861-878.

[5] H. Lu, J. Qi, B. Wang and M. Zhang, Pullback D-attractors for non-autonomous stochastic fractional power

dissipative equations on R^n. Discrete and Continuous Dynamical Systems Series A, 39(2) (2019), 683-706 (PDF).

[6] L. Zhang, M. Han, M. Zhang and C. Khalique, A new type of solitary wave solution appearing for the mKdV equation under singular perturbations. International Journal of Bifurcation and Chaos, 30(11) (2020), 2050162, 1-14.

[7] X. Zhang, Y. Tian, M. Zhang and Y. Qi, Mathematical studies on generalized Burgers Huxley equation and its singularly perturbed form: Existence of traveling wave solutions. Nonlinear Dynamics, 2024, 3, 2625-2634.

[8] X. Sun and M. Zhang, Dynamics of a quartic Korteweg-de Vries equation with multiple dissipations via an Abelian integral approach. Chaos, 35, 083118, 2025. (Editor's pick PDF)

PART III: HILBERT'S 16TH PROBLEM

[1] J. Li, M. Zhang and S. Li, Bifurcations of Limit Cycles in a Z_2-Equiveriant Planar Polynomial Vector Field of Degree 7. International Journal of Bifurcation and Chaos, 16(4) (2006), 925-943.