Personal Info
Scientific Research
Education and Teachi
Social Position
Publications
Training

赵昆

Zhao Kun

Department： Mathematics

Discipline： Mathematics

Duty：

Prof. Title： Professor

Tutor： Ph.D. Advisor

Tel：

Fax：

E-Mail： kzhao@hrbeu.edu.cn

Postcode： 150001

Add：哈尔滨市南岗区南通大街145号

Profile

I am a Professor of Mathematics at the Harbin Engineering University. Broadly speaking, I am interested in applied mathematics. The goal of my research is to utilize analytical and computational tools to understand the qualitative and quantitative properties of mathematical models, and how the properties can help interpret natural phenomena and solve real-world problems. Alongside mathematical research, I am keen to educate and train young talents.

Education

2004/08-2009/12, Ph.D. in Mathematics, Georgia Institute of Technology
2001/09-2004/07, M.S. in Mathematics, University of Science and Technology of China
1997/09-2001/07, B.S. in Mathematics, University of Science and Technology of China

Experience

2024/07-now, Professor, School of Mathematical Sciences, Harbin Engineering University
2018/07-2024/06, Associate Professor, Department of Mathematics, Tulane University
2012/07-2018/06, Assistant Professor, Department of Mathematics, Tulane University
2011/08-2012/06, Visiting Assistant Professor, Department of Mathematics, University of Iowa
2009/09-2011/07, Postdoctoral Researcher, Mathematical Biosciences Institute, Ohio State University

Research Fields

Applied Mathematics, Analysis of Partial Differential Equations, Mathematical Biology (chemotaxis, vasculogenesis, angiogenesis, tumor growth, infectious diseases), Fluid Dynamics (buoyancy flow, porous medium flow, multi-phase flow, magnetohydrodynamics, bio-fluid flow)

Projects

Academic Communication

I collaborate with scientists around the world, including mathematical modellers, numerical analysts, computational scientists, and applied analysts.

Admissions

Students who are interested in applied mathematics with strong analytical or numerical background are welcome to contact me for possible positions in the M.S. or Ph.D. program in the School of Mathematical Sciences at Harbin Engineering University.

Course For Undergraduate

Fall 2024, Mathematical Analysis I, Harbin Engineering University

Course For Postgraduate

Practical Teaching

Teaching Research

Social Position

2024/08-2028/07, Council Member, Heilongjiang Mathematical Society
2020/08-now, Associate Editor, Annals of Applied Mathematics

Patent

Book

Article

[1] Z. Feng, Y. Tang, W. Wang, K. Zhao and N. Zhu, On a chemotaxis model with singular sensitivity: convergence rate towards spiky steady state, Discrete and Continuous Dynamical Systems, re-submited after minor revision.
[2] Z. Feng, K. Zhao and S. Zhou, Existence and stability of boundary spike layer solutions of an attractive chemotaxis model with singular sensitivity and nonlinear consumption rate of chemical stimuli, Physica D: Nonlinear Phenomena, re-submited after minor revision.
[3] Y. Zeng and K.Zhao, Global stability of a system of viscous balance laws arising from chemotaxis with dynamic boundary flux, Journal of Differential Equations, in press.
[4] P. Fuster-Aguilera and K. Zhao, Dynamical behavior of a logarithmically sensitive chemotaxis model under time-dependent boundary conditions, European Journal of Applied Mathematics, 2024, DOI: https://doi.org/10.1017/S0956792524000329
[5] L. Xue, M. Zhang, K. Zhao and X. Zheng, On 2D incompressible and density-dependent Navier-Stokes equations: global stabilization under dynamic Couette flow, Computational and Applied Mathematics, Vol. 43, Article No. 432, 2024.
[6] L. Xue, M. Zhang and K. Zhao, Stability of aerostatic equilibria in porous medium flows, Journal of Differential Equations, Vol. 378, pp. 678-706, 2023.
[7] J. Wu and K. Zhao, On 2D incompressible Boussinesq systems: global stabilization under dynamic boundary data, Journal of Differential Equations, Vol. 367, pp. 246-289, 2023.
[8] Z. Wang, A. Yang and K. Zhao, Wave propagation and stabilization in the Boussinesq-Burgers system, Physica D: Nonlinear Phenomena, Vol. 447, 2023.
[9]H. Peng and K. Zhao, On a hyperbolic-parabolic chemotaxis system, Mathematical Biosciences and Engineering, Vol. 20, pp. 7802-7827, 2023.
[10] L. Xue, M. Zhang, K. Zhao and X. Zheng, Global stability under dynamic boundary conditions of a nonlinear PDE model arising from reinforced random walks, Communications in Nonlinear Science and Numerical Simulation, Vol. 117, pp. 106913, 2023.
[11] Y. Zeng and K. Zhao, Asymptotic Behavior of Solutions to a chemotaxis-logistic model with transitional end-states, Journal of Differential Equations, Vol. 336, pp. 1-43, 2022.
[12] L. Xue, M. Zhang, K. Zhao and X. Zheng, Controlled dynamics of a chemotaxis model with logarithmic sensitivity by physical boundary conditions, Electronic Research Archive, Vol. 30, pp. 4530-4552, 2022.
[13] X. Zheng, K. Zhao, T. Jackson and J. Lowengrub, Tumor grows towards lower extracellular matrix conductivity regions under Darcy's law and steady morphology, Journal of Mathematical Biology, Vol. 85, 2022.
[14] H. Zhang and K. Zhao, On 3D Hall-MHD equations with fractional Laplacians: global well-posedness, Journal of Mathematical Fluid Mechanics, Vol. 23, 2021.
[15] B. Li, F. Wang, L. Xue, K. Yang and K. Zhao, On the Cahn-Hilliard-Brinkman equations in

: global well-posedness, Annals of Applied Mathematics, Vol. 37, pp. 513-536, 2021.
[16] T. Li, D. Wang, F. Wang, Z. Wang and K. Zhao, Large time behavior and diffusion limit for a system of balance laws from chemotaxis in multi-dimensions, Communications in Mathematical Sciences, Vol. 19, pp. 229-272, 2021.
[17] D. Wang, Z. Wang and K. Zhao, Cauchy problem of a system of parabolic conservation laws arising from the singular Keller-Segel model in multi-dimensions, Indiana University Mathematics Journal, Vol. 70, pp. 1-47, 2021.
[18] Z. Feng, J. Xu, L. Xue and K. Zhao, Initial and boundary value problem for a system of balance laws from chemotaxis: global dynamics and diffusion limit, Annals of Applied Mathematics, Vol. 37, pp. 61-110, 2021.
[19] F. Wang, L. Xue, K. Zhao and X. Zheng, Global stabilization and boundary control of generalized Fisher/KPP equation and application to diffusive SIS model, Journal of Differential Equations, Vol. 275, pp. 391-417, 2021.
[20] N. Zhu, Z. Liu, F. Wang and K. Zhao, Asymptotic dynamics of a system of conservation laws from chemotaxis, Discrete and Continuous Dynamical Systems, Vol. 41, pp. 813-847, 2021.
[21] B. Li, F. Wang and K. Zhao, Large time dynamics of 2D semi-dissipative Boussinesq systems, Nonlinearity, Vol. 33, pp. 2481-2501, 2020.
[22] J. Fan, L. Jing, G. Nakamura and K. Zhao, Qualitative analysis of an integrated chemotaxis-fluid model: global existence and extensibility criterion, Communications in Mathematical Sciences, Vol. 18, pp. 809-836, 2020.
[23] S. Li, J. Wu and K. Zhao, On the degenerate Boussinesq equations on surfaces, Journal of Geometric Mechanics, Vol. 12, pp. 107-140, 2020.
[24] Y. Zeng and K. Zhao, Erratum to "Optimal Decay Rates for a Chemotaxis Model with Logistic Growth, Logarithmic Sensitivity and Density-dependent Production/Consumption Rate" [J. Differential Equations (2020) 1379-1411], Journal of Differential Equations, Vol. 269, pp. 6359-6363, 2020.
[25] L. Tao, J. Wu, K. Zhao and X. Zheng, Stability near hydrostatic equilibrium to the 2D Boussinesq equations without thermal diffusion, Archive for Rational Mechanics and Analysis, Vol. 237, pp. 585-630, 2020.
[26] N. Zhu, Z. Liu, F. Wang and K. Zhao, Explicit decay rates for a generalized Boussinesq-Burgers system, Applied Mathematics Letters, Vol. 100, 106054, 7 pp, 2020.
[27] Y. Zeng and K. Zhao, Optimal decay rates for a chemotaxis model with logistic growth, logarithmic sensitivity and density-dependent production/consumption rate, Journal of Differential Equations, Vol. 268, pp. 1379-1411, 2020.
[28] Y. Zeng and K. Zhao, On the Keller-Segel-Fisher/KPP system, Discrete and Continuous Dynamical Systems, Vol. 39, pp. 5365--5402, 2019.
[29] L. Rebholz, D. Wang, Z. Wang, C. Zerfas and K. Zhao, Initial boundary value problems for a system of parabolic conservation laws arising from chemotaxis in multi-dimensions, Discrete and Continuous Dynamical Systems, Vol. 39, pp. 3789-3838, 2019.
[30] L. Guan, D. Li, K. Wang and K. Zhao, On a class of nonlocal SIR models, Journal of Mathematical Biology, Vol. 78, pp. 1581-1604, 2019.
[31] N. Zhu, Z. Liu and K. Zhao, Non blowup of a generalized Boussinesq-Burgers system with nonlinear dispersion relation and large data, Physica D: Nonlinear Phenomena, Vol. 392, pp. 81-98, 2019.
[32] J. Fan and K. Zhao, Improved extensibility criteria and long-time behavior of a coupled chemotaxis-fluid model, Discrete and Continuous Dynamical Systems - Series B, Vol. 23, pp. 3949-3967, 2018.
[33] N. Zhu, Z. Liu, V. Martinez and K. Zhao, Global Cauchy problem of a system of parabolic conservation laws arising from a Keller-Segel type chemotaxis model, SIAM Journal on Mathematical Analysis, Vol. 50, pp. 5380-5425, 2018.
[34] C. Doering, J. Wu, K. Zhao and X. Zheng, Long-time behavior of two-dimensional Boussinesq equations without buoyancy diffusion, Physica D: Nonlinear Phenomena, Vol. 376/377, pp. 144-159, 2018.
[35] H. Peng, Z. Wang, K. Zhao and C. Zhu, Boundary layers and stabilization of the singular Keller-Segel model, Kinetic and Related Models, Vol. 11, pp. 1085-1123, 2018.
[36] V. Martinez, Z. Wang and K. Zhao, Asymptotic and viscous stability of large-amplitude solutions of a hyperbolic system arising from biology, Indiana University Mathematics Journal, Vol. 67, pp. 1383-1424, 2018.
[37] N. Zhu, Z. Liu, and K. Zhao, On the Boussinesq-Burgers equations driven by dynamic boundary conditions, Journal of Differential Equations, Vol. 264, pp. 2287-2309, 2018.
[38] V. Martinez and K. Zhao, Analyticity and dynamics of a Navier-Stokes-Keller-Segel system on bounded domains, Dynamics of Partial Differential Equations, Vol. 14, pp. 125-158, 2017.
[39] L. Rebholz, C. Zerfas and K. Zhao, Global in time analysis and sensitivity analysis for the reduced NS-alpha model of incompressible flow, Journal of Mathematical Fluid Mechanics, Vol. 19, pp. 445-467, 2017.
[40] Q. Hou, Z. Wang and K. Zhao, Boundary layers on a hyperbolic system arising from chemotaxis, Journal of Differential Equations, Vol. 261, pp. 5035-5070, 2016.
[41] T. Li and K. Zhao, Analysis of non-isentropic compressible Euler equations with relaxation, Journal of Differential Equations, Vol. 259, pp. 6338-6367, 2015.
[42] D. Li, R. Pan and K. Zhao, Quantitative decay of a hybrid type chemotaxis model with large data, Nonlinearity, Vol. 28, pp. 2181-2210, 2015.
[43] H. Li and K. Zhao, Initial boundary value problems for a system of hyperbolic balance laws arising from chemotaxis, Journal of Differential Equations, Vol. 258, pp. 302-338, 2015.
[44] J. Fan and K. Zhao, Global dynamics of a coupled chemotaxis-fluid model on bounded domains, Journal of Mathematical Fluid Mechanics, Vol. 16, pp. 351-364, 2014.
[45] J. Fan and K. Zhao, A note on a 3D haptotaxis model of cancer invasion, Applied Mathematics Research Express, Vol. 2014, 74-86, 2014.
[46] J. Fan and K. Zhao, Global Cauchy problem of 2D generalized MHD equations, Journal of Mathematical Analysis and Applications, Vol. 420, pp. 1024-1032, 2014.
[47] J. Lowengrub, E.S. Titi and K. Zhao, Analysis of a mixture model of tumor growth, European Journal of Applied Mathematics, Vol. 24, pp. 691-734, 2013.
[48] S. Dai, D. Li and K. Zhao, Finite-time quenching of competing species with constrained border evaporation, Discrete and Continuous Dynamical Systems - Series B, Vol. 18, pp. 1275-1290, 2013.
[49] Z. Wang and K. Zhao, Global dynamics and diffusion limit of a one-dimensional repulsive chemotaxis model, Communications on Pure and Applied Analysis, Vol. 12, pp. 3027-3046, 2013.
[50] J. Fan and K. Zhao, Blow up criteria for a hyperbolic-parabolic system arising from chemotaxis, Journal of Mathematical Analysis and Applications, Vol. 394, pp. 687-695, 2012.
[51] T. Li, R. Pan and K. Zhao, Global dynamics of a chemotaxis model on bounded domains with large data, SIAM Journal on Applied Mathematics, Vol. 72, pp. 417-443, 2012.
[52] K. Zhao, Large time behavior of density-dependent incompressible Navier-Stokes equations on bounded domains, Journal of Mathematical Fluid Mechanics, Vol. 14, pp. 471-483, 2012.
[53] K. Zhao, Long-time dynamics of a coupled Cahn-Hilliard-Boussinesq system, Communications in Mathematical Sciences, Vol. 10, pp. 735-749, 2012.
[54] T. Li and K. Zhao, Global existence and long-time behavior of entropy weak solutions to a quasilinear hyperbolic blood flow model, Networks and Heterogeneous Media, Vol. 6, pp. 625-646, 2011.
[55] D. Li, T. Li and K. Zhao, On a hyperbolic-parabolic system modeling repulsive chemotaxis, Mathematical Models and Methods in Applied Sciences, Vol. 21, pp. 1631-1650, 2011.
[56] T. Li and K. Zhao, On a quasilinear hyperbolic system in blood flow modeling, Discrete and Continuous Dynamical Systems - Series B, Vol. 16, pp. 333-344, 2011.
[57] K. Zhao, Global regularity for a coupled Cahn-Hilliard-Boussinesq system on bounded domains, Quarterly of Applied Mathematics, Vol. 69, pp. 331-356, 2011.
[58] M. Lai, R. Pan and K. Zhao, Initial boundary value problem for 2D viscous Boussinesq equations, Archive for Rational Mechanics and Analysis, Vol. 199, pp. 739-760, 2011.
[59] K. Zhao, 2D inviscid heat conductive Boussinesq system in a bounded domain, Michigan Mathematical Journal, Vol. 59, pp. 329-352, 2010.
[60] R. Pan and K. Zhao, 3D compressible Euler equations with damping in a bounded domain, Journal of Differential Equations, Vol. 246, pp. 581-596, 2009.
[61] R. Pan and K. Zhao, Initial boundary value problem for compressible Euler equations with damping, Indiana University Mathematics Journal, Vol. 57, pp. 2257-2282, 2008.

Honors

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Personal Information

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Research

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Teaching

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Publications

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Training

Current Graduate Students
[1] Yue Huang (Ph.D. in Mathematics, Harbin Engineering University) 2024/09-
[2] Sinchita Lahiri (Ph.D. in Mathematics, Tulane University) 2020/08-
[3] Yingying Li (M.S. in Mathematics, Harbin Engineering University) 2025/09-
[4] Yi Sun (M.S. in Mathematics, Harbin Engineering University) 2024/09-

Past Graduate Students
[1] Min Zhang (Ph.D. in Mathematics, Harbin Engineering University) 2020/09-2024/07, co-advised
Current Position: Lecturer, Department of Mathematics, Northeastern University, China
[2] Jiao Xue (Ph.D. in Mathematics, South China University of Technology) 2019/08-2020/08, co-advised
  Current Position: Associate Professor, Department of Mathematics, South China University of Technology
[3] Zefu Feng (Ph.D. in Mathematics, South China University of Technology) 2019/08-2021/01, co-advised
  Current Position: Associate Professor, School of Mathematical Sciences, Chongqing Normal University
[4] Neng Zhu (Ph.D. in Mathematics, South China University of Technology) 2016/08-2017/08, co-advised
  Current Position: Associate Professor, Department of Mathematics, Nanchang University
[5] Padi Fuster Aguilera (Ph.D. in Mathematics, Tulane University) 2016/08-2021/05
  Current Position: Postdoctoral Researcher, Department of Mathematics, University of Colorado-Boulder

赵昆