Linghai Zhang
Associate Professor of Mathematics
Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania 18015
Telephone: 610-758-4116. Fax: 610-758-3767. Email: liz5@lehigh.edu
EDUCATION
- BA: Department of Mathematics, Beijing Normal University 1986
- MA: Division of Applied Mathematics,
Beijing Institute of Applied Physics and Computational Mathematics 1989
- Ph.D: Department of Mathematics, The Ohio State University 1999
AWARDS
- Franz Summer Research Award: Lehigh University
- Graduate Teaching Associate Awards: The Ohio State University
- Howard Hughs Medical Institute.
Title: Modeling local synaptic control in neural coincidence detectors.
(co-PI: Michael Burger, Department of Biological Sciences, Lehigh University)
- Reidler Research Foundation.
Title: Modeling propagation of nerve impulses arising from
synaptically coupled neuronal networks
- Faculty Research Grants
RESEARCH INTERESTS
- Synaptically Coupled Neuronal Networks, Mathematical Biology
- Differential Equations and Dynamical Systems
- Sharp Rates of Decay of Global Solutions of PDEs
SELECTED PUBLICATIONS
- Linghai Zhang, On stability of traveling wave solutions in
synaptically coupled neuronal networks.
Differential and Integral Equations, 16(2003), number 5, 513-536.
- Linghai Zhang, Existence, uniqueness and exponential stability
of traveling wave solutions of some integral differential equations arising
from neuronal networks.
Journal of Differential Equations, 197(2004), number 1, 162-196.
- Linghai Zhang, Traveling waves of a singularly perturbed system of
integral-differential equations arising from neuronal networks.
Journal of Dynamics and Differential Equations, 17(2005),
number 3, 489-522.
- Linghai Zhang, Dynamics of neuronal waves. Mathematische Zeitschrift,
255(2007), number 2, 283-321.
- Linghai Zhang, How do synaptic coupling and spatial temporal delay
influence traveling waves in nonlinear nonlocal neuronal networks?
SIAM Journal on Applied Dynamical Systems, 6(2007), number 3, 597-644.
- Linghai Zhang, New results of a general n-dimensional incompressible
Navier-Stokes equations. Journal of Differential Equations, (2008).
- Linghai Zhang, Solutions to some open problems in n-dimensional fluid
dynamics. in Progress in Nonlinear Analysis Research. (2008), 73-139.
Here are some recent colloquium lectures given at Lehigh University
or at international conferences in mathematics:
2.pdf, 3.pdf,
4.pdf, 5.pdf, 6.pdf,
7.pdf, 8.pdf
For a complete list of my publications,
please go to the website of the American Mathematical Society (AMS):
www.ams.org/mathscinet
SELECTED RESEARCH TOPICS
- Mathematical neuroscience: nonlinear waves
(including traveling waves, periodic waves and spiral waves) modeled with
nonlinear singularly perturbed systems of integral differential equations.
I investigate the influence of biological mechanisms on wave forms
and wave speeds of many different model equations arising from
mathematical neuroscience (in particular, synaptically coupled neuronal networks)
- partial differential equations and infinite-dimensional dynamical systems:
Cauchy problems for nonlinear partial differential equations
In particular, my research covers the following model equations
- nonlocal integral differential equations
- nonlinear Korteweg-de Vries-Burgers equations
- nonlinear Benjamin-Bona-Mahony-Burgers equations
- n-dimensional incompressible Navier-Stokes equations
- n-dimensional incompressible Magnetohydrodynamics equations
POSITIONS HELD
- Associate Professor: Department of Mathematics, Lehigh University.
14 East Packer Avenue, Bethlehem, Pennsylvania 18015 USA. August 2008-now.
- Visiting Assistant Professor: Mathematical Biosciences Institute,
The Ohio State University. 231 West 18th Avenue, Columbus, Ohio 43210 USA.
September-December, 2006
- Assistant Professor: Department of Mathematics, Lehigh University.
14 East Packer Avenue, Bethlehem, Pennsylvania 18015 USA. August 2002-August 2008
- Dunham Jackson Assistant Professor:
School of Mathematics, University of Minnesota. 206 Church Street Southeast,
Minneapolis, Minnesota 55455 USA. 1999-2002
- Graduate Teaching Associate:
Department of Mathematics, The Ohio State University.
231 West 18th Avenue, Columbus, Ohio 43210 USA. 1994-1999
- Research Assistant: Division of Applied Mathematics,
Beijing Institute of Applied Physics and Computational Mathematics.
P. O. Box: 8009, Beijing 100088 People's Republic of China. 1989-1994
TEACHING
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