Projects

Research grants
 

PI: Critical regularity, selection dynamics, and condensation in nonlinear balance laws: funding National Science Foundation (2021--2023). DMS2135470.

PI - Data-driven Optimal Control modeling of PDEs,  TrAC research project.      

Core co-PI Presidential interdisciplinary Research Initiative (PIRI), Iowa State University,  (PI: Sarkar Soumik), 
Translational AI Center for Research and Education (TrAC), 2021-2024.

PI: Simons Foundation Collaboration Travel Grant, 2018--2023.

PI: Critical regularity, selection dynamics, and condensation in nonlinear balance laws
funding National Science Foundation (2018-2021). DMS18-12666

PI:  Recovery of High Frequency Wave Fields, Kinetic Theory of Photons and Entropy Satisfying Methods:
funding National Science Foundation (2013-2017). DMS13-12636. 

 

  • H. Liu
    Global orientation dynamics for liquid crystalline polymers, Physica D. 228 (2007), 122-129.

    T. Li and H. Liu (2007)
    Critical thresholds in a relaxation model for travel flows, to appear in J. Indiana Univ.

    T. Li and H. Liu (2006)

    Critical thresholds in relaxation systems with resonance of characteristic speeds, submitted.

    M. D. Francesco, K. Fellner and H. Liu (2006)

    A non-local conservation law with nonlinear `radiation inhomogeneity. Submitted JHDE

    H. Liu
    Wave Breaking in a class of nonlocal dispersive wave equations, Journal of Nonlinear Math Phys. 13 (3), (2006), 441-466.

    H. Liu
    Critical Thresholds in the Semiclassical Limit of 2-D Rotational Schr\"dinger Equations, ZAMP. 57 (2006), 42-58.

  • H. Liu and C. Sparber (2007)

    Rigorous Derivation of the Hydrodynamical Equations for Rotating Superfluids, to appear in M3AS.

    H. Liu and Z.M. Wang (2007)
    Superposition of multi-valued solutions in high frequency wave dynamics, to appear in Journal of Scientific Computing.

    H. Liu and Z.M. Wang,
    A field space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations
    Journal of Computational Physics, 225 (2007), 591-614.

    H. Liu and Z.M. Wang
    Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations,
    Applied Numerical Mathematics, 57 (2007), 821-836.

    H. Liu, S. Osher and R. Tsai,

  • A. Haseena and H. Liu (2007)
    Formulation and analysis of alternating evolution (AE) schemes for hyperbolic conservation laws, Submitted to SINUM.

    A. Haseena and H. Liu (2007)

    A numerical study for the performance of the Runge-Kutta Finite Difference

    method based on different numerical Hamiltonians, submitted to CICP.

    H. Liu (2007)
    An Alternating Evolution Approximation to Systems of Hyperbolic Conservation laws, submitted to JHDE.

    G.-Q. Chen  and  H.L. Liu 
    Concentration and Cavitation in Solutions of the Euler equations for nonisentropic fluids as the pressure vanishes Physics. D.  189 (2004), 141--165.

  • H. Liu and C. Sparber (2007)

    Rigorous Derivation of the Hydrodynamical Equations for Rotating Superfluids, to appear in M3AS.

    H. Liu and Z.M. Wang (2007)
    Superposition of multi-valued solutions in high frequency wave dynamics,� to appear in Journal of Scientific Computing.
    H. Liu and Z.M. Wang,
    A field space-based level set method for computing multi-valued solutions to 1D Euler-Poisson equations
    Journal of Computational Physics, 225 (2007), 591�614.
    H. Liu and Z.M. Wang
    Computing multi-valued velocity and electric fields for 1D Euler-Poisson equations,
    Applied Numerical Mathematics, 57 (2007), 821-836.

    H. Liu, S. Osher and R. Tsai,

  • C. Liu and H. Liu,

    Boundary conditions for the microscopic FENE models, preprint

    H. Liu
    Global orientation dynamics for liquid crystalline polymers, Physica D. 228 (2007), 122-129.

    H. Liu, H. Zhang and P.W. Zhang
    Axial Symmetry and Classification of Stationary Solutions of  Doi-Onsager Equation on the Sphere with Maier-Saupe Potential, Comm. Math. Sci. 3 (2), (2005), 201-218.

  • T. Li and H. Liu (2007)
    Critical thresholds in a relaxation model for travel flows, to appear in J. Indiana Univ.

    T. Li and H. Liu (2006)

    Critical thresholds in relaxation systems with resonance of characteristic speeds, submitted.

    T.  Li  and  H. Liu
    Stability of a traffic flow model with  nonconvex relaxation,  Comm. Math. Sci., Vol 3 (2), (2005), 101--118.

    H. Liu (2004) 
    Relaxation Dynamics, Scaling Limits and Convergence of Relaxation Schemes,   Spring Verlag.

     H.L. Liu  
    Asymptotic Stability of Relaxation Shock Profiles for Hyperbolic Conservation Laws,   J. Diff. Equ.  192 (2003), 285--307.