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. J. Dyn. Diff. Equat., 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 J. Appl. Dyn. Syst., 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 J. Appl. Math., 75(1) (2015), 114-135.

[4] M. Zhang, Asymptotic expansions and numerical simulations on I-V relations on I-V relations via a Poisson-Nernst-Planck system with zero permanent function. Rocky MT. J. Math. 45(5) (2015), 1681-1708.

[5] Y. Jia, W. Liu and M. Zhang, Poisson-Nernst-Planck systems for ion flow with Bikerman's local hard-sphere

potential: Ion size and valence effects. Discrete Contin. Dyn. Syst. Ser. B, 21(6) (2016), 1775-1802.

[6] P. W. Bates, W. Liu, H. Lu and M. Zhang: Ion size and valence effects on on ionic flows via

Poisson-Nernst-Planck systems. Commun. Math. Sci., 15(4) (2017), 881 − 901.

[7] 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 J. Appl. Dyn. Syst., 16(1) (2017), 410-430.

[8] J. Zhang, D. Acheampong and M. Zhang, Effects on ionic flows from finite ion sizes via Poisson-Nernst-Planck models with non-local excess chemical potentials. Mol. Based. Math. Biol, 5(1) (2017), 58-77.

[9] H. Lu, J. Li, J. Shackelford, J. Vorenberg and M. Zhang, Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman’s local hard-sphere potential: Analysis without electroneutrality boundary conditions.Discrete Contin. Dyn. Syst. Ser. B, 23(4) (2018), 1623-1643.

[10] M. Zhang, Boundary layer effects on ionic flows via classical Poisson-Nernst-Planck systems. Compute. Math. Biophys., 6 (2018), 14-27.

[11] R. Aitbayev, P. W. Bates, H. Lu, L. Zhang and M. Zhang, Mathematical studies of Poisson-Nernst-Planck systems: dynamics of ionic flows without electroneutrality conditions. J. Comput. Appl. Math., 362 (2019), 510-527.

[12] P. W. Bates, J. Chen and M. Zhang, Dynamics of ionic flows via Poisson-Nernst-Planck systems with local excess chemical potentials: Competition between cations. Math. Biosci. Eng. 17(4) (2020), 3736-3766. PDF

[13] Z. Wen, L. Zhang and M. Zhang, Dynamics of classical Poisson-Nernst-Planck systems with multiple cations and boundary layers. J. Dyn. Diff. Equat., 33 (2021), 211-234.

[14] M. Zhang, Competition between cations via Poisson-Nernst-Planck systems with nonzero but small permanent charges. Membranes, 11 (2021), 236. (MDPI open access) PDF

[15] 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

[16] 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. J. Nonlinear Sci., 31 (2021), 1-62. DOI: 10.1007/s00332-021-09715-3 AAM PDF (This is a post-peer-review, pre-copyedit version of an article published in the Journal of Nonlinear Science. The final authenticated version is available online at http://dx.doi.org/10.1007/s00332-021-09715-3)

[17] 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

[18] Y. Bao, J. Chen, L. Zhang and M. Zhang, Higher order expansions in finite ion size via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential. J. Appl. Anal. Comput. 12(3) (2022), 907-931.

[19] Y. Wang, L. Zhang and M. Zhang, Studies on individual fluxes via Poisson-Nernst-Planck models with small permanent charges and partial electroneutrality conditions. J. Appl. Anal. Comput.,12(1) (2022), 87-105.

[20] 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. https://doi.org/10.1007/s12346-022-00672-0

[21] J. Chen and M. Zhang, Boundary layer effects on ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes. Discrete Contin. Dyn. Syst. Ser. B, 27(10) (2022), 6197-6216. doi:10.3934/dcdsb.2021312

[22] X. Deng, Y. Jia and M. Zhang, Studies on I-V relations via Poisson-Nernst-Planck systems with multiple cations and small permanent charges. J. Appl. Anal. Comput., 12(3) (2022), 932-951.

[23] M. Zhang, Qualitative properties of zero-current ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes. Discrete Contin. Dyn. Syst. Ser. B, 27(12) (2022), 6989-7019.

[24]Y. Fu, W. Liu, H. Mofidi and M. Zhang, Finite ion size effects on ionic flows via Poisson-Nernst-Planck systems: Higher order contributions. J. Dan. Diff. Equal., 35 (2023), 1585-1609.

[25] M. Zhang, Existence and local uniqueness of classical Poisson-Nernst-Planck systems with multi-component permanent charges and multiple cations. Discrete Contin. Dyn. Syst. Ser. S, 16 (3&4) (2023), 725-752. doi:10.3934/dcdss.2022134

[26] Y. Wang, L. Zhang and M. Zhang, Mathematical analysis on current-voltage relations via classical Poisson-Nernst-Planck systems with nonzero permanent charges under relaxed electroneutrality boundary conditions. Membranes, (2023), 13, 131.

[27] Y. Wang and M. Zhang, Finite ion size effects on I-V relations via Poisson-Nernst-Planck system with two cations: A case study. Math. Biosci. Eng., 21(2) (2024), 1899-1916.

[28] X. Liu, L. Zhang and M. Zhang, Studies on ionic flows via Poisson-Nernst-Planck system with Bikerman's local hard-sphere potentials under relaxed boundary conditions. Mathematics, (2024), 12, 1182.

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.

J. Differ. 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 Anal., 128 (2015), 176-198.

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

equation with multiplicative noise on an unbounded domain. Commun. Math. Sci., 14(1) (2016), 273-295.

[4] P. W. Bates, J. Li and M. Zhang, Singular fold with real noise. Discrete Contin. Dyn. Syst. Ser. B, 21(7) (2016), 2091-2107.

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

Ginzburg-Landau equation. Discrete Contin. Dyn. Syst. Ser. A, 37(5) (2017), 2539-2564.

[6] H. Lu, P. W. Bates, W. Chen and M. Zhang, The spectral collocation method for efficiently solving PDEs with fractional Laplacian. Adv. Comput. Math., 44(3) (2018), 861-878.

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

dissipative equations on R^n. Discrete Contin. Dyn. Syst. Ser. A, 39(2) (2019), 683-706.

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

[9] H. Lu and M. Zhang, Dynamics of non-autonomous fractional Ginzburg-Landau equations driven by colored noise. Discrete Contin. Dyn. Syst. Ser. B, 25(9) (2020), 3553-3576.

[10] H. Lu, J. Li and M. Zhang, Spectral methods for two-dimensional space and time fractional Bloch-Torrey equations. Discrete Contin. Dyn. Syst. Ser. B, 25(9) (2020), 3357-3371.

[11] K Zhu, J. Li, Y. Xie and M. Zhang, Dynamics of non-autonomous fractional reaction-diffusion equations on R^{N} driven by multiplicative noise. Discrete Contin. Dyn. Syst. Ser. B, 26(10) (2021), 5681-5705. doi:10.3934/dcdsb.2020376

[12] H. Lu, J. Li and M. Zhang, Stochastic dynamics of non-autonomous fractional Ginzburg-Landau equations on R^3. Discrete Contin. Dyn. Syst. Ser. B, 27(11), (2022), 6943-6968.

[13] H. Lu, L. Wang, L. Zhang and M. Zhang, Limiting dynamics of non-autonomous stochastic Ginzburg-Landau equations on thin domains. J. Appl. Anal. Comput., 11(5) (2021), 2313-2333.

[14] X. Liu, L. Zhang and M. Zhang, Studies on pull-in instability of an electrostatic MEMS actuator: Dynamical system approach. J. Appl. Anal. Comput., 12(2) (2022), 850-861.

[15] H. Lu, L. Wang and M. Zhang, Dynamics of fractional stochastic Ginzburg-Landau equation driven by nonlinear noise. Mathematics, 10 (23), (2022), 4485.

[16] H. Lu and M. Zhang, Dynamics of stochastic Ginzburg-Landau equations driven by colored noise on thin domains. J. Nonlinear Modeling and Analysis, 5(2), (2023), 288-310.

[17] H. Lu and M. Zhang, Upper semi-continuity and regularity of random attractors for stochastic fract. J. Appl. Anal. Comput. (2024), 14 (2), 816-846.

[18] H. Lu, L. Wang and M. Zhang, Studies on invariant measures of fractional stochastic delay Ginzburg-Landau equations on R^n. Math. Biosci. Eng. (2024), 21 (4), 5456-5498.

[19] Y. Jia, C. Lin and M. Zhang, Finite-time stability of discrete descriptor systems with time-varying delay and nonlinear uncertainties. J. Appl. Anal. Comput. (to appear).

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. Int. J. Bifurcation Chaos, 16(4) (2006), 925-943.

PUBLICATIONS WITH STUDENTS & VISITING SCHOLARS

WITH PHD STUDENTS

[1] P. W. Bates, Jianing Chen and M. Zhang, Dynamics of ionic flows via Poisson-Nernst-Planck systems with local excess chemical potentials: Competition between cations. Math. Biosci. Eng. 17(4) (2020), 3736-3766.

[2] Jianing 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.

[3] Y. Bao, Jianing Chen, L. Zhang and M. Zhang, Higher order expansions in finite ion size via Poisson-Nernst-Planck systems with Bikerman's local hard-sphere potential. J. Appl. Anal. Comput. (to appear)

[4] Jianing Chen and M. Zhang, Boundary layer effects on ionic flows via Poisson-Nernst-Planck systems with nonuniform ion sizes. Discrete Contin. Dyn. Syst. Ser. B (to appear)

[5] Jianing 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.

WITH MASTER STUDENTS

[1] H. Lu, J. Li, Joseph Shackelford, Jeremy Vorenberg and M. Zhang, Ion size effects on individual fluxes via Poisson-Nernst-Planck systems with Bikerman’s local hard-sphere potential: Analysis without electroneutrality boundary conditions. Discrete Contin. Dyn. Syst. Ser. B, 23(4) (2018), 1623-1643.

[2] J. Zhang, Daniel Acheampong and M. Zhang, Effects on ionic flows from finite ion sizes via Poisson-Nernst-Planck models with non-local excess chemical potentials. Mol. Based. Math. Biol, 5(1) (2017), 58-77.

WITH VISITING SCHOLARS

[1] Zhenshu Wen (Huaqiao University, China, Aug. 2018--Aug. 2019), L. Zhang and M. Zhang, Dynamics of classical Poisson-Nernst-Planck systems with multiple cations and boundary layers. J. Dyn. Diff. Equat., 33 (2021), 211-234.

[2] P. W. Bates, Zhenshu Wen and M. Zhang, Small permanent charge effects on individual fluxes via via classical Poisson-Nernst-Planck systems with multiple cations. J. Nonlinear Science, 31 (2021), 1-62.

[3] Zhenshu 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.

[4] Jianing Chen, Yiwei Wang (Zhejiang Sci-Tech University, China, Aug. 2019--Aug. 2020), 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.

[5] Yiwei Wang, L. Zhang and M. Zhang, Studies on individual fluxes via Poisson-Nernst-Planck models with small permanent charges and partial electroneutrality conditions. (J. Appl. Anal. Comput., to appear)