Nonlinear Waves: Overview and Problems

The subject of nonlinear hyperbolic waves is surveyed, with an emphasis on the discussion of a number of open problems.

[1]  Tai-Ping Liu,et al.  Convergence to diffusion waves of solutions for viscous conservation laws , 1987 .

[2]  Juan A. Zufiria,et al.  Bubble competition in Rayleigh–Taylor instability , 1988 .

[3]  Z. Xin,et al.  Viscous limits for piecewise smooth solutions to systems of conservation laws , 1992 .

[4]  Andrew J. Majda,et al.  Nonlinear development of instabilities in supersonic vortex sheets I. The basic kink modes , 1987 .

[5]  Qiang Zhang,et al.  A numerical study of bubble interactions in Rayleigh–Taylor instability for compressible fluids , 1990 .

[6]  Hervé Gilquin,et al.  Glimm's scheme and conservation laws of mixed type , 1989 .

[7]  G. Caginalp An analysis of a phase field model of a free boundary , 1986 .

[8]  J. Glimm,et al.  AnS matrix theory for classical nonlinear physics , 1986 .

[9]  David H. Sharp,et al.  The dynamics of bubble growth for Rayleigh-Taylor unstable interfaces , 1987 .

[10]  E. Laitone,et al.  Mathematical Theory of Compressible Fluids , 1964 .

[11]  L. F. Henderson On the refraction of longitudinal waves in compressible media , 1988 .

[12]  John A. Trangenstein,et al.  Conservation laws of mixed type describing three-phase flow in porous media , 1986 .

[13]  Andrew J. Majda,et al.  Nonlinear kink modes for supersonic vortex sheets , 1989 .

[14]  L. Hsiao,et al.  The Riemann problem and interaction of waves in gas dynamics , 1989 .

[15]  James Glimm,et al.  The continuous structure of discontinuities , 1989 .

[16]  Mary F. Wheeler,et al.  Numerical simulation in oil recovery , 1988 .

[17]  David H. Sharp,et al.  Late stage of Rayleigh-Taylor instability , 1961 .

[18]  Chen Guiqiang,et al.  OVERTAKING OF SHOCKS OF THE SAME KIND IN THE ISENTROPIC STEADY SUPERSONIC PLANE FLOW , 1987 .

[19]  Zhouping Xin,et al.  Stability of viscous shock waves associated with a system of nonstrictly hyperbolic conservations laws , 1992 .

[20]  A. J. MAJDA,et al.  Numerical Study of the Mechanisms for Initiation of Reacting Shock Waves , 1990, SIAM J. Sci. Comput..

[21]  P. R. Woodward Simulation of the Kelvin-Helmholtz instability of a supersonic slip surface with the Piecewise-Parabolic Method (PPM) , 1984 .

[22]  Helge Holden,et al.  On the Riemann problem for a prototype of a mixed type conservation law , 1987 .

[23]  James Glimm,et al.  The interaction of nonlinear hyperbolic waves , 1988 .

[24]  G. Caginalp,et al.  Stefan and Hele-Shaw type models as asymptotic limits of the phase-field equations. , 1989, Physical review. A, General physics.

[25]  Gunduz Caginalp,et al.  Phase Field Models and Sharp Interface Limits: Some Differences in Subtle Situations , 1991 .

[26]  T. Ting,et al.  Wave curves for the riemann problem of plane waves in isotropic elastic solids , 1987 .

[27]  Gunduz Caginalp,et al.  The role of microscopic anisotropy in the macroscopic behavior of a phase boundary , 1986 .

[28]  Juan A. Zufiria,et al.  Vortex‐in‐cell simulation of bubble competition in a Rayleigh–Taylor instability , 1988 .

[29]  K. I. Read,et al.  Experimental investigation of turbulent mixing by Rayleigh-Taylor instability , 1984 .

[30]  Tai-Ping Liu,et al.  Nonlinear Stability of Shock Waves for Viscous Conservation Laws , 1985 .

[31]  X. Garaizar,et al.  The small anisotropy formulation of elastic deformation , 1989 .

[32]  Tai-Ping Liu,et al.  The inviscid limit for the Navier-Stokes equations of compressible, isentropic flow with shock data , 1989 .

[33]  T. Teichmann,et al.  Mathematical Theory of Compressible Fluid Flow , 1958 .

[34]  R. L. Rabie,et al.  The polymorphic detonation , 1979 .

[35]  Tai-Ping Liu Hyperbolic conservation laws with relaxation , 1987 .

[36]  G. Caginalp The Dynamics of a Conserved Phase Field System: Stefan-like, Hele-Shaw, and Cahn-Hilliard Models as Asymptotic Limits , 1990 .

[37]  R. Menikoff,et al.  The Riemann problem for fluid flow of real materials , 1989 .