- I am a Professor at the Department of Mathematics , ISU. My general research interests lie in the area of computational and applied mathematics. I have conducted research in analysis and numerical computation of hyperbolic balance laws, kinetic transports, and Schroedinger equations with applications in fluids, plasma and polymers.
- I am also a member of the CFD center here at ISU, and a research associate at the Ames Laboratory (DOE facility).
- Associate Editor for the journal: Journal of Mathematical Analysis and Applications
- This
Spring I am teaching
Math
517, Finite Difference Methods.
Recent Publications
·
H. Liu and J. Yan
The Direct
Discontinuous Galerkin (DDG) method for diffusion
with interface corrections , Commun.
Comput. Phys. 8(3) (2010), 541--564.
·
H. Liu and J. Ralston
Recovery
of high frequency wave fields from phase space based measurements, Multiscale Model. Simul. 8(2)
(2010), 622--644.
·
H. Liu and J. Ralston
Recovery
of high frequency wave fields for the acoustic wave equation, Multiscale Model. Simul. 8(2)
(2009), 428--444.
·
P. Degond and H. Liu
Kinetic
models for polymers with inertial effects, Networks and Heterogeneous
Media. 4(4)(2009), 625--647.
·
H. Liu, E. Tadmor and
D. Wei
Global regularity
of the 4D Restricted Euler equations, Physics D. published online July
2009.
·
Tong Li and H. Liu
Critical
thresholds in hyperbolic relaxation systems, J. Diff. Equ.
247(1) (2009), 33--48.
·
H. Liu and Zhongming
Wang
A Bloch
band based level set method for computing the semi-classical limit of Schroedinger equations, J. Comp. Phys. 228(9) (2009),
3326--3344.
·
Tong Li and H. Liu
Critical
thresholds in a relaxation system with resonance of characteristic speeds,
Discrete and Continuous Dynamical Systems, Series A. 24(2) (2009), 511-521.
·
H. Liu and J. Yan
The
Direct Discontinuous Galerkin (DDG) methods for
diffusion problems, SIAM Journal on Numerical Analysis. 47(1) (2009),
675--698.
·
H. Liu
On discreteness of
the Hopf equation, Acta Math. Appl. Sin. Engl. Ser. 24
(2008), no. 3, 423--440.
·
H. Liu and Z.M. Wang
Superposition of
multi-valued solutions in high frequency wave dynamics, Journal of
Scientific Computing, 35(2-3) (2008), 192--218.
·
H. Liu and C. Sparber
Rigorous
Derivation of the Hydrodynamical Equations for
Rotating Superfluids , Mathematical Models and
Methods in Applied Sciences, 18(5) (2008), 689--706.
·
T. Li and H. Liu
Critical
thresholds in a relaxation model for travel flows, Indiana Univ. Math.
Journal, 57(3) (2008), 1409--1430.
·
M. D. Francesco, K. Fellner
and H. Liu
A
non-local conservation law with nonlinear radiation inhomogeneity. J.
Hyperbolic Differ. 5(1) (2008), 1--23.
·
Chun Liu and H. Liu
Boundary
Conditions for the Microscopic FENE Models. SIAM J. Appl. Math. 68 (5)
(2008), 1304--1315.