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,
Multi-valued solution and level set methods in computational high frequency wave propagation, Commun. Comput. Phys. 1(5) (2006), 765-804.
H. Liu
Wave Breaking in a class of nonlocal dispersive wave equations, Journal of Nonlinear Math Phys. 13 (3), (2006), 441-466.
H. Liu and J. Yan
A local discontinuous {G}alerkin method for the {K}orteweg-de {V}ries equation with boundary effect, JCP 215 (2006), 197-218.
H. Liu
Critical Thresholds in the Semiclassical Limit of- 2-D Rotational Schr\"{o}dinger Equations, ZAMP. 57 (2006), 42-58.
H.L. Liu, L.-T. Cheng and S. Osher
A level set framework for capturing multi-valued solutions to nonlinear first-order equations, J. Sci. Comp. 29(3) (2006), 353-373.
S. Jin, H.L. Liu, S. Osher and R. Tsai
Computing multi-valued physical observables for the high frequency limit of symmetric hyperbolic systems, JCP, 210(2005), 498-518.
S. Jin, H.L. Liu, S. Osher and R. Tsai
Computing multivalued physical observables for the semiclassical limit of the Schrodinger equations,
Journal of Computational Physics, 205(1) (2005), 222-241.
H.L. Liu and M. Slemrod
KdV Dynamics in the Plasma-Sheath Transition, Appl. Math. Lett. 17 ( 2004) 401--419.
L.T. Cheng, H.L. Liu and S. Osher
Computational high frequency wave propagation using the level set method, with applications to the semi-classical limit of Schroedinger equations, Comm. Math. Sci. Vol 1, No. 3 (2003), 593--621.