Vanishing viscosity approximation to hyperbolic conservation laws

[1]  G. M.,et al.  Partial Differential Equations I , 2023, Applied Mathematical Sciences.

[2]  P. Lax.  Hyperbolic systems of conservation laws II , 1957 .

[3]  P. Lax,et al.  Systems of conservation laws , 1960 .

[4]  O. Oleinik.  Discontinuous solutions of non-linear differential equations , 1963 .

[5]  J. Glimm.  Solutions in the large for nonlinear hyperbolic systems of equations , 1965 .

[6]  S. Kružkov.  FIRST ORDER QUASILINEAR EQUATIONS IN SEVERAL INDEPENDENT VARIABLES , 1970 .

[7]  C. Dafermos.  Polygonal approximations of solutions of the initial value problem for a conservation law , 1972 .

[8]  R. J. Diperna.  Global existence of solutions to nonlinear hyperbolic systems of conservation laws , 1976 .

[9]  C. Dafermos.  Generalized Characteristics and the Structure of Solutions of Hyperbolic Conservation Laws , 1976 .

[10]  J. Smoller.  Shock Waves and Reaction-Diffusion Equations , 1983 .

[11]  P. Souganidis,et al.  Asymptotic Series and the Methods of Vanishing Viscosity , 1985 .

[12]  Editors , 1986, Brain Research Bulletin.

[13]  R. LeVeque.  Numerical methods for conservation laws , 1990 .

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

[15]  Chi-Wang Shu,et al.  Efficient Implementation of Weighted ENO Schemes , 1995 .

[16]  Wang Chi-Shu,et al.  Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws , 1997 .

[17]  A. Bressan,et al.  Error Bounds for a Deterministic Version of the Glimm Scheme , 1998 .

[18]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[19]  Centro internazionale matematico estivo. Session,et al.  Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , 1998 .

[20]  E. Tadmor.  Approximate solutions of nonlinear conservation laws , 1998 .

[21]  S. Yu,et al.  Zero-Dissipation Limit of Solutions with Shocks for Systems of Hyperbolic Conservation Laws , 1999 .

[22]  A. Bressan,et al.  L1 Stability Estimates for n×n Conservation Laws , 1999 .

[23]  D. Serre.  Systems of conservation laws , 1999 .

[24]  A. Bressan.  Hyperbolic Systems of Conservation Laws , 1999 .

[25]  A. Bressan.  Hyperbolic systems of conservation laws : the one-dimensional Cauchy problem , 2000 .

[26]  A. Bressan,et al.  Vanishing Viscosity Solutions of Nonlinear Hyperbolic Systems , 2001, math/0111321.

[27]  H. Holden,et al.  Front Tracking for Hyperbolic Conservation Laws , 2002 .

[28]  Paul Dupuis,et al.  Second Order Numerical Methods for First Order Hamilton-Jacobi Equations , 2002, SIAM J. Numer. Anal..

[29]  R. LeVeque.  Finite Volume Methods for Hyperbolic Problems: Characteristics and Riemann Problems for Linear Hyperbolic Equations , 2002 .

[30]  Zhangxin Chen,et al.  Fluid Flow and Transport in Porous Media: Mathematical and Numerical Treatment , 2002 .

[31]  On the convergence rate of vanishing viscosity approximations , 2003, math/0307141.

[32]  Zhiliang Xu,et al.  Conservative Front Tracking with Improved Accuracy , 2003, SIAM J. Numer. Anal..

[33]  Mathematisches Forschungsinstitut Oberwolfach,et al.  Hyperbolic Conservation Laws , 2004 .

[34]  C. M. Dafermos,et al.  Hyberbolic [i.e. Hyperbolic] conservation laws in continuum physics , 2005 .

[35]  P. Lax.  Hyperbolic systems of conservation laws , 2006 .