Linghai Zhang
Department of Mathematics, Lehigh University
Telephone: 610-758-4116. Fax: 610-758-3767.
EDUCATION
Ph.D: Department of Mathematics, The Ohio State University. 1994 - 1999
POSITIONS HELD
Associate Professor: Department of Mathematics, Lehigh University. 2008 - present.
Assistant Professor: Department of Mathematics, Lehigh University. 2002 - 2008.
Dunham Jackson Assistant Professor: School of Mathematics, University of Minnesota. 1999 - 2002.
Assistant Researcher: Beijing Institute of Applied Physics and Computational Mathematics. 1989 - 1994.
RESEARCH INTERESTS
The Exact Limits and Improved Decay Estimates with Sharp Rates of All Order Derivatives
of the Global Smooth Solutions (or Global Weak Solutions) of
Nonlinear Systems of Fluid Dynamics Equations
(Including n-Dimensional Magnetohydrodynamics Equations, n-Dimensional Incompressible Navier-Stokes Equations,
n-Dimensional Newton-Boussinesq Equations, Several Other Similar Equations), Two-Dimensional Dissipative Quasi-Geostrophics Equation and
Two-Dimensional Nonlinear Singular System of Differential Equations Arising from Geostrophics,
One-Dimensional Nonlinear Dissipative Dispersive Wave Equations
(Including Korteweg-de Vries-Burgers Equation, Benjamin-Bona-Mahony-Burgers Equation and Benjamin-Ono-Burgers Equation,
where the nonlinear functions at least include u^2+u^3+u^4).
The Existence and Stability of Traveling Pulse Solutions of Nonlinear Singularly Perturbed Systems of Integral Differential Equations
Arising from Synaptically Coupled Neuronal Networks
(and Nonlinear Singularly Perturbed System of Reaction Diffusion Equations Arising from Mathematical Neuroscience)
Explicit Representations of Bounded Smooth Traveling Wave Solutions of Five Kinds of Nonlinear Evolution Equations with Strong Physical Backgrounds
Mathematical Analysis of Wave Speeds of Traveling Waves
PUBLICATIONS OTHER PEOPLE CITED OFTEN
Linghai Zhang, Decay of solutions of generalized Benjamin-Bona-Mahony equations.
Acta Mathematica Sinica, New Series. 10(1994), 428-438.
Linghai Zhang, Decay estimates for the solutions of some nonlinear evolution equations.
Journal of Differential Equations, 116(1995), 31-58.
Linghai Zhang, Sharp rate of decay of solutions to 2-dimensional Navier-Stokes equations.
Communications in Partial Differential Equations,
20(1995), 119-127.
Linghai Zhang, Decay of solution of generalized Benjamin-Bona-Mahony-Burgers equations in n-space dimensions.
Nonlinear Analysis, Theory, Methods and Applications, 25(1995), 1343-1369.
Linghai Zhang, On stability of traveling wave solutions in synaptically coupled neuronal networks.
Differential and Integral Equations, 16(2003), 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), 162-196.
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), 597-644.
More Papers on n-Dimensional Magnetohydrodynamics Equations and n-Dimensional Incompressible Navier-Stokes Equations are coming.
TEACHING
I have taught both undergraduate and graduate classes at Lehigh University: including
Mathematics 21: Calculus One
Mathematics 22: Calculus Two
Mathematics 23: Calculus Three
Mathematics 205: Linear Methods (Differential Equations and Linear Algebra)
Mathematics 295: Introduction to Dynamical Systems in Mathematical Biology
Mathematics 301: Principles of Mathematical Analysis
Mathematics 320: Ordinary Differential Equations
Mathematics 405: Partial Differential Equations
Mathematics 435: Functional Analysis
Mathematics 450: Topics in Applied Mathematics
and many other classes.
PH.D STUDENTS and POSTDOCS
Melissa Stoner received Ph.D in May 2011 (research in mathematical neuroscience).
Alan Dyson received Ph.D in May 2019 (research in mathematical neuroscience).
Nan Lu (Ph.D from Georgia Institute of Technology) received post doctoral training 2014 - 2016.
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.
Also read Psalm 103!
Proverbs: Chapter 3: 5-6
Trust in the Lord with all your heart
and lean not on your own understandings;
in all your ways acknowledge him,
and he will make your paths straight.