Free Access
Volume 37, Number 1, January/February 2003
Page(s) 1 - 39
Published online 15 March 2003
  1. S. Benzoni-Gavage, Stability of semi-discrete shock profiles by means of an Evans function in infinite dimensions. J. Dynam. Differential Equations 14 (2002) 613-674. [CrossRef] [MathSciNet]
  2. S. Benzoni-Gavage, D. Serre and K. Zumbrun, Alternate Evans functions and viscous shock waves. SIAM J. Math. Anal. 32 (2001) 929-962. [CrossRef] [MathSciNet]
  3. M. Bultelle, M. Grassin and D. Serre, Unstable Godunov discrete profiles for steady shock waves. SIAM J. Numer. Anal. 35 (1998) 2272-2297. [CrossRef] [MathSciNet]
  4. C. Chainais-Hillairet and E. Grenier, Numerical boundary layers for hyperbolic systems in 1-D. ESAIM: M2AN 35 (2001) 91-106. [CrossRef] [EDP Sciences]
  5. C. Dafermos, Hyperbolic conservation laws in continuum physics. Springer (2000).
  6. R. A. Gardner and K. Zumbrun, The gap lemma and geometric criteria for instability of viscous shock profiles. Comm. Pure Appl. Math. 51 (1998) 797-855. [CrossRef] [MathSciNet]
  7. M. Gisclon and D. Serre, Étude des conditions aux limites pour un système strictement hyberbolique via l'approximation parabolique. C.R. Acad. Sci. Paris Sér. I Math. 319 (1994) 377-382.
  8. M. Gisclon and D. Serre, Conditions aux limites pour un système strictement hyperbolique fournies par le schéma de Godunov. RAIRO Modél. Math. Anal. Numér. 31 (1997) 359-380. [MathSciNet]
  9. P. Godillon, Necessary condition of spectral stability for a stationary Lax-Wendroff shock profile. Preprint UMPA, ENS Lyon, 295 (2001).
  10. P. Godillon, Linear stability of shock profiles for systems of conservation laws with semi-linear relaxation. Phys. D 148 (2001) 289-316. [CrossRef] [MathSciNet]
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  12. E. Grenier and F. Rousset, Stability of one-dimensional boundary layers by using Green's functions. Comm. Pure Appl. Math. 54 (2001) 1343-1385. [CrossRef] [MathSciNet]
  13. G. Jennings, Discrete shocks. Comm. Pure Appl. Math. 27 (1974) 25-37. [CrossRef] [MathSciNet]
  14. C.K.R.T. Jones, Stability of the travelling wave solution of the FitzHugh-Nagumo system. Trans. Amer. Math. Soc. 286 (1984) 431-469. [CrossRef] [MathSciNet]
  15. T. Kato, Perturbation theory for linear operators. Springer-Verlag (1985).
  16. T.-P. Liu, On the viscosity criterion for hyperbolic conservation laws, in Viscous profiles and numerical methods for shock waves (Raleigh, NC, 1990), pp. 105-114. SIAM, Philadelphia, PA (1991).
  17. T.-P. Liu and Z. Xin, Overcompressive shock waves, in Nonlinear evolution equations that change type. Springer-Verlag, New York, IMA Vol. Math. Appl. 27 (1990) 139-145.
  18. T.-P. Liu and S.-H. Yu, Continuum shock profiles for discrete conservation laws. I. Construction. Comm. Pure Appl. Math. 52 (1999) 85-127. [CrossRef] [MathSciNet]
  19. T.-P. Liu and S.-H. Yu, Continuum shock profiles for discrete conservation laws. II. Stability. Comm. Pure Appl. Math. 52 (1999) 1047-1073. [CrossRef] [MathSciNet]
  20. A. Majda and J. Ralston, Discrete shock profiles for systems of conservation laws. Comm. Pure Appl. Math. 32 (1979) 445-482. [CrossRef] [MathSciNet]
  21. C. Mascia and K. Zumbrun, Pointwise green's function bounds and stability of relaxation shocks. Indiana Univ. Math. J. 51 (2002) 773-904. [CrossRef] [MathSciNet]
  22. D. Michelson, Discrete shocks for difference approximations to systems of conservation laws. Adv. in Appl. Math. 5 (1984) 433-469. [CrossRef] [MathSciNet]
  23. S. Schecter and M. Shearer, Transversality for undercompressive shocks in Riemann problems, in Viscous profiles and numerical methods for shock waves (Raleigh, NC, 1990), pp. 142-154. SIAM, Philadelphia, PA (1991).
  24. D. Serre, Remarks about the discrete profiles of shock waves. Mat. Contemp. 11 (1996) 153-170. Fourth Workshop on Partial Differential Equations, Part II (Rio de Janeiro, 1995). [MathSciNet]
  25. D. Serre, Discrete shock profiles and their stability, in Hyperbolic problems: theory, numerics, applications, Vol. II (Zürich, 1998), pp. 843-853. Birkhäuser, Basel (1999).
  26. D. Serre, Systems of conservation laws. 1. Cambridge University Press, Cambridge (1999). Hyperbolicity, entropies, shock waves. Translated from the 1996 French original by I.N. Sneddon.
  27. K. Zumbrun and P. Howard, Pointwise semigroup methods and stability of viscous shock waves. Indiana Univ. Math. J. 47 (1998) 741-871. [CrossRef] [MathSciNet]
  28. K. Zumbrun and D. Serre, Viscous and inviscid stability of multidimensional planar shock fronts. Indiana Univ. Math. J. 48 (1999) 937-992. [CrossRef] [MathSciNet]

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