Advanced Search
Article Contents
Article Contents

The relative entropy method for the stability of intermediate shock waves; the rich case

Abstract Related Papers Cited by
  • M.-J. Kang and one of us [2] developed a new version of the relative entropy method, which is efficient in the study of the long-time stability of extreme shocks. When a system of conservation laws is rich, we show that this can be adapted to the case of intermediate shocks.
    Mathematics Subject Classification: 35L65, 35L67.


    \begin{equation} \\ \end{equation}
  • [1]

    S. Benzoni-Gavage, D. Serre and K. Zumbrun, Alternate Evans functions and viscous shock waves, SIAM J. Math. Anal., 32 (2001), 929-962.doi: 10.1137/S0036141099361834.


    M.-J. Kang and A. Vasseur, Criteria on contractions for entropic discontinuities of systems of conservation laws, reprint, arXiv:1505.02245 (2015).


    P. D. Lax, Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10 (1957), 537-566.doi: 10.1002/cpa.3160100406.


    N. Leger, $L^2$-stability estimates for shock solutions of scalar conservation laws using the relative entropy method, Arch. Rational Mech. Anal., 199 (2011), 761-778.doi: 10.1007/s00205-010-0341-7.


    N. Leger and A. Vasseur, Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-BV perturbations, Arch. Ration. Mech. Anal., 201 (2011), 271-302.doi: 10.1007/s00205-011-0431-1.


    T.-P. Liu, Pointwise convergence to $N$-waves for solutions of hyperbolic conservation laws, Bull. Inst. Math. Acad. Sinica, 15 (1987), 1-17.


    A. Majda, The stability of multidimensional shock fronts, Memoirs Amer. Math. Soc., 41 (1983), iv+95 pp.doi: 10.1090/memo/0275.


    A. Majda, The existence of multidimensional shock fronts, Memoirs Amer. Math. Soc., 43 (1983), v+93 pp.doi: 10.1090/memo/0281.


    D. Serre, Richness and the classification of quasilinear hyperbolic systems. Multidimensional hyperbolic problems and computations (Minneapolis, MN, 1989), IMA Vol. Math. Appl., 29, Springer, New York, (1991), 315-333.doi: 10.1007/978-1-4613-9121-0_24.


    D. Serre, Systems of Conservation Laws, II, Cambridge Univ. Press, 2000.


    D. Serre, The structure of dissipative viscous system of conservation laws, PhysicaD, 239 (2010), 1381-1386.doi: 10.1016/j.physd.2009.03.014.


    D. Serre, Long-time stability in systems of conservation laws, using relative entropy/energy, Arch. Ration. Mech. Anal., 219 (2016), 679-699.doi: 10.1007/s00205-015-0903-9.


    D. Serre, A. Vasseur, $L^2$-type contraction for systems of conservation laws, Journal de l'École polytechnique; Mathématiques, 1 (2014), 1-28.doi: 10.5802/jep.1.

  • 加载中

Article Metrics

HTML views() PDF downloads(201) Cited by(0)

Access History

Other Articles By Authors



    DownLoad:  Full-Size Img  PowerPoint