Research Interests:

· Geometric Singular Perturbation Theory (GSPT)

· Applications of GSPT to Poisson-Nernst-Planck type models

· Bifurcation theory for planar polynomial vector space

· Mathematical biology

· Partial differential equations

Selected Publications and Preprints

· H. Lu, S. Lv and M. Zhang: Fourier spectral approximations to the dynamics of 3D fractional complex Ginzburg-Landau equation

(Submitted)

· P. W. Bates, W. Liu, H. Lu and M. Zhang: Ion size and valence effects on ionic flows via Poisson-Nernst-Planck.

(Submitted)

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

J. Differential Equations (to appear)

· H. Lu, P. W. Bates, S. Lv and M. Zhang: Stochastic dynamics of 3D fractional Ginzburg-Landau equation with multiplicative noise on an unbounded domain.

Commun. Math. Sci. (to appear)

· H. Lu, P. W. Bates, J. Xin and M. Zhang: Asymptotic behavior of stochastic fractional power dissipative equations on R^n.

(Submitted)

· S. Ji, W. Liu and M. Zhang: Effects of (small) permanent charge and channel geometry on ionic flows via classical Poisson-Nernst-Planck models.

SIAM J. on Appl. Math., 75 (1) 114-135 (2015)

· M. Zhang: Asymptotic expansions and numerical simulations on I-V relations via a Poisson-Nernst-Planck system with zero permanent charge function.

Rocky Mountain J. Math. (to appear)

· 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. on Appl. Dyn. Syst., 12(3) 1613-1648 (2013)

· 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. Dynamics and Differential Equations, 24(4) 985-1004 (2012)

· M. Zhang and S. Li: Distribution of Limit Cycles in Z_2-Equivariant Planar Polynomial Vector Field of Degree 7.

J. Kunming University of Science and Technology (Science and Technology) 31(6): 111-113 (2006)

· D. Kong, H. Guo and M. Zhang: Classification of Z_2-equivariant planar Hamiltonian phase portrait.

J. Science Information, 4: 139-140 (2006)

· J. Li, M. Zhang and S. Li: Bifurcations of Limit Cycles in Z_2-Equivariant Planar Polynomial Vector Field of Degree 7.

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

Teaching

Summer 2015: Math 411 (Abstract Algebra II)

Class meets at 12:40pm-2:30pm in 114 EBH on TWF

Office hours: TWF 11:30-12:30 and by appointment

Syllabus

For more details about the final, please refer to Class Page or my Personal Page!