Welcome to the homepage of Linghai Zhang

Linghai Zhang
Department of Mathematics, Lehigh University, Bethlehem, Pennsylvania
Telephone: 610-758-4116. Fax: 610-758-3767. Email: liz5@lehigh.edu

EDUCATION

Ph.D: Department of Mathematics, The Ohio State University. 1994-1999

RESEARCH INTERESTS

Mathematical Neuroscience
Differential Equations and Dynamical Systems

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, Influence of sodium currents on speeds of traveling wave fronts in synaptically coupled neuronal networks. Physica D, (2010). (with Ping-Shi Wu and Mellisa A. Stoner) PhD
Linghai Zhang, How do neurobiological mechanisms influence speeds of traveling waves in mathematical neurosciences? SIAM Journal on Applied Mathematics. (with Ping-Shi Wu and Mellisa A. Stoner)
Linghai Zhang, New results of a general n-dimensional incompressible Navier-Stokes equations. Journal of Differential Equations, 245(2008), number 11, 3470-3502.
Linghai Zhang, The exact limits and decay estimates of global strong solutions of $n$-dimensional fluid dynamics equations. to appear.
Linghai Zhang, Exact limits of global strong solutions of some nonlinear dissipative partial differential equations arising from $n$-dimensional fluid dynamics. to appear.
Linghai Zhang, Solutions to Some Open Problems in n-Dimensional Fluid Dynamics, in ``Progress in Nonlinear Analysis Research''. Editor-in-Chief: Erik T. Hoffmann. Nova Science Publishers, INC. 2009. Pages 69-135.
Linghai Zhang, Traveling Waves Arising from Synaptically Coupled Neuronal Networks, in ``Differential Equations: Analysis and Applications''. Editor-in-Chief: Frank Columbus. Nova Science Publishers, INC. 2010.

For a complete list of my research publications, please go to the website of the American Mathematical Society (AMS): www.ams.org/mathscinet.
Here are my Curriculum Vitae, Research Statement, Teaching Statement and Service Statement. Here are some recent mathematics talks: 1. 2. 3. 4. 5. 6. 7. 8. 9.

SELECTED RESEARCH TOPICS

Mathematical neuroscience: traveling waves modeled with nonlinear singularly perturbed systems of integral differential equations. I investigate the influence of biological mechanisms on existence and stability of traveling wave solutions and wave speeds of model equations arising from synaptically coupled neuronal networks. I have introduced two very important concepts: speed index functions and stability index functions, to study the existence, uniqueness and stability of traveling waves in mathematical neuroscience.
Global solutions of Cauchy problems for nonlinear nonhomogeneous dissipative partial differential equations arising from n-dimensional fluid dynamics. In particular, I investigate the exact limits and decay estimates with sharp rates of the global solutions. I have invented a very general method to establish stronger and broader results than before, under weaker condiitons on the model equations.

POSITIONS HELD

Associate Professor: Department of Mathematics, Lehigh University. 14 East Packer Avenue, Bethlehem, Pennsylvania 18015 USA. August 2008 - present.
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

TEACHING

m205

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SOME OTHER WEBSITES:

Psalm 23

The Lord is my shepherd, I shall not be in want.
He makes me lie down in green pastures,
he leads me beside quiet waters, he restores my soul.
He guides me in paths of righteousness for his name's sake.
Even though I walk through the valley of the shadow of death,
I will fear no evil, for you are with me;
your rod and your staff, they comfort me.
You prepare a table before me in the presence of my enemies.
You anoint my head with oil; my cup overflows.
Surely goodness and love will follow me all the days of my life,
and I will dwell in the house of the Lord forever.

Modified on Wednesday, July 1, 2009.