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
The courses I have been teaching at Lehigh University are listed below:
* Calculus sequences (Mathematics 021-022-023 and Mathematics 075-076)
* Differential Equations and Linear Algebra (Mathematics 205)
* Introduction to Dynamical Systems in Mathematical Biology (Mathematics 295)
* Ordinary Differential Equations (Mathematics 320)
* Mathematical Models and Their Formulation (Mathematics 341)
* Partial Differential Equations sequence (Mathematics 405-406)
* Introduction to Functional Analysis (Mathematics 435)
* Dynamical Systems and Mathematical Biology (Mathematics 450)
* Nonlinear Partial Differential Equations (Mathematics 450)
To return to the Department of Mathematics, please click
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SOME OTHER WEBSITES:
- Center for BioDynamics, Boston University
- Department of Mathematics, Carnegie Mellon University
- Department of Mathematics, Cornell University
- School of Mathematics, Georgia Institute of Technology
- Department of Mathematics, Harvard University
- Department of Mathematics, Indiana University
- Department of Mathematics, Lehigh University
- Department of Mathematics, Massachusetts Institute of Technology
- Courant Institute of Mathematical Sciences, New York University
- Department of Mathematics, The Ohio State University
- Department of Mathematics, The Pennsylvania State University
- Department of Mathematics, Princeton University
- Department of Mathematics, Rutgers University
- Department of Mathematics, Stanford University
- Department of Mathematics, The University of California in Los Angeles
- Department of Mathematics, The University of Chicago
- Department of Mathematics, The University of Illinois at Urbana Champaign
- Department of Mathematics, The University of Maryland
- Department of Mathematics, The University of Michigan
- Institute for Mathematics and its Applications, The University of Minnesota
- School of Mathematics, The University of Minnesota
- Department of Mathematics, The University of Pittsburgh
- Department of Mathematics, The University of Texas at Austin
- Department of Mathematics, The University of Utah
- Department of Applied Mathematics, The University of Washington
- Department of Mathematics, The University of Wisconsin
- Department of Mathematics, Yale University
- Department of Mathematics, Peking University, China
- Department of Mathematics, Tsinghua University, China
- Institute of Information and Mathematical Sciences, Massey University, New Zealand
- Department of Mathematics, The University of Nottingham
- Mathematical Institute, Tohoku University, Japan
-
Archive for Rational Mechanics and Analysis
- Communications in Partial Differential Equations
- Journal of Differential Equations
- Journal of Functional Analysis
- Physica D
- SIAM Journal on Applied Dynamical Systems
- SIAM Journal on Applied Mathematics
- Transactions of the American Mathematical Society
- Workshop on Nonlocal Integral Differential Equations in Mathematics and Biology.
Mathematical Biosciences Institute, The Ohio State University. March 6-8, 2003.
- Conference on Mathematical Neuroscience
(A Satellite Activity of the International Congress of Mathematicians 2006 - NEUROMATH 2006)
(an activity of the project: Shaping new directions in Mathematics for Science and Society)
at Sant Julia de Loria, Principat d'Andorra. September 1-4, 2006.
- International Conference on Applied Mathematics and Interdisciplinary Research.
Nankai Institute of Mathematics, Nankai University. Tianjin, The People's Republic of China. June 12-15, 2006.
- International Conference: Nonlinear Waves - Theory and Applications.
Tsinghua University, Beijing, The People's Republic of China. June 9-12, 2008.
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.