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Hyperbolic Conservation Laws, Stability of Discrete and Viscous Shock Profiles

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.

G.-Q. Chen  and  H.L. Liu 
Formation of Delta-Shocks and Vacuum States in the Vanishing Pressure Limit of Solutions to the Isentropic Euler Equations SIAM J. Math Anal.  34 (2003), 925--938.

J. Pan and H.L. Liu
Convergence rates to traveling waves of viscous conservation laws with dispersion J. Diff. Equ.  187 (2003), 337--358.

 H. L. Liu
The l^1 Global Decay to Discrete Shocks for Scalar Monotone Schemes, Math. Comp. 72 (2003), 227-245

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.

J. Pan, H.L. Liu
On stability of travelling waves of Burgers-Fisher equation, Ann. Differential Equations, 14 (1998), 37--47.

 H.L. Liu
Nonlinear stability of shock profiles for non-convex model equations with degenerate shock, J. Partial Differential Equations 11(1998), 209--230.

H.L. Liu and J. Wang
Asymptotic stability of stationary discrete shocks of Lax-Friedrichs scheme for non-convex conservation laws, Japan J. Indust. Appl. Math. 15 (1998), 1-16.

H.L. Liu
Asymptotic stability of shock profiles for non-convex convection diffusion equation, Appl. Math. Lett. 10 (1997), 129-134.

H.L. Liu, J. Wang
Decay rate for perturbations of stationary  discrete shocks for convex scalar conservation laws, Math. Comp. 66 (1997), 69-84.

 H. L. Liu
Asymptotic properties of solutions to nonconvex hyperbolic conservation laws(Chinese), Gaoxiao Yingyong Shuxue Xuebao Ser. A 11 (1996), 277--282.

 H.L. Liu, J. Wang
Asymptotic stability of traveling wave solution for a hyperbolic system with relaxation terms, Beijing Math. 2 (1996), 119-130.

 H. L. Liu, J. Wang
Nonlinear stability of stationary discrete profiles of non-convex scalar conservation laws, Math. Comp. 65 (1996), 1137-1153.

 H. Liu and J. Pan
Decay rate for perturbations of viscous shock profiles for non-convex convection-diffusion equation, Appl. Functional Anal. 2 (1995), 171-176.

H. L. Liu
The interactions of shock waves of nonstrictly hyperbolic systems, Acta Math. Scientia, 12 (1992), 312-336.