High Frequency Wave Propagation and Geometric Motion

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.

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 multi-valued physical observables for the semiclassical limit of the Schroedinger equation, JCP, 205 (2005), 222-241.

H.T.  Fan and  H.L. Liu 
Pattern Formation, Wave Propagation and Stability in Conservation Laws  with  Slow Diffusion and Fast Reaction
 Journal of Hyperbolic Differential Equations, 1(4) (2004) 605--626.

 H.L. Liu, L.-T. Cheng and S. Osher (2003)
A level set framework for capturing  multi-valued solutions to nonlinear first-order equations, submitted.

 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.

L.T. Cheng, H.L. Liu and S. Osher
High frequency wave propagation in Schroedinger equations using the Level Set method, preprint, 2003.