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Stability of Solutions to Hyperbolic Systems of Conservation Laws

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REFERENCES

  1. P. Baiti and H. K. Jenssen, “On the front tracking algorithm, ” J. Math. Anal. Appl. (in press).

  2. A. Bressan, “Contractive metrics for nonlinear hyperbolic systems, ” Indiana Univ. Math. J., 37, 409–421 (1988).

    Google Scholar 

  3. A. Bressan, “Global solutions of systems of conservation laws by wave-front tracking, ” J. Math. Anal. Appl., 170, 414–432 (1992).

    Google Scholar 

  4. A. Bressan, “The unique limit of the Glimm scheme, ” Arch. Ration. Mech. Anal., 130, 205–230 (1995).

    Google Scholar 

  5. A. Bressan and R. M. Colombo, “The semigroup generated by 2×2 conservation laws, ” Arch. Ration. Mech. Anal., 133, 1–75 (1995)

    Google Scholar 

  6. A. Bressan, G. Crasta, and B. Piccoli, “Well posedness of the Cauchy problem for n × n systems of conservation laws, ” Preprint S.I.S.S.A., Trieste (1996).

  7. A. Bressan and P. Goatin, “Oleinik type estimates and uniqueness for n × n conservation laws, ” Preprint S.I.S.S.A., Trieste (1997).

  8. A. Bressan and P. LeFloch, “Uniqueness of weak solutions to hyperbolic systems of conservation laws, ” Arch. Ration. Mech. Anal., 140, 301–317 (1997).

    Google Scholar 

  9. A. Bressan and M. Lewicka, “A uniqueness condition for hyperbolic systems of conservation laws, ” Preprint S.I.S.S.A., Trieste (1998).

  10. A. Bressan, T. P. Liu and T. Yang, “L1 stability estimates for n×n conservation laws, ” Arch. Ration. Maech. Anal. (in press).

  11. C. Dafermos, “Polygonal approximations of solutions of the initial value problem for a conservation law, ” J. Math. Anal. Appl., 38, 33–41 (1972).

    Google Scholar 

  12. R. J. DiPerna, “Global existence of solutions to nonlinear hyperbolic systems of conservation laws, ” J. Diff. Equat., 20, 187–212 (1976).

    Google Scholar 

  13. R. J. DiPerna, “Uniqueness of solutions to hyperbolic conservation laws, ” Indiana Univ. Math. J., 28, 137–188 (1979).

    Google Scholar 

  14. J. Glimm, “Solutions in the large for nonlinear hyperbolic systems of equations, ” Comm. Pure Appl. Math., 18, 697–715 (1965).

    Google Scholar 

  15. H. K. Jenssen, “Blowup for systems of conservation laws, ” Preprint (1998).

  16. F. John, “Formation of singularities in one-dimensional nonlinear wave propagation, ” Comm. Pure Appl. Math., 27, 377–405 (1974).

    Google Scholar 

  17. S. Kruzkov, “First-order quasilinear equations with several space variables, ” Mat. Sb., 123, 228–255 (1970); English translation: Math. USSR Sb., 10, 217–273 (1970).

    Google Scholar 

  18. P. D. Lax, “Hyperbolic systems of conservation laws. II, ” Comm. Pure Appl. Math., 10, 537–566 (1957).

    Google Scholar 

  19. T. P. Liu, “Uniqueness of weak solutions of the Cauchy problem for general 2× 2 conservation laws, ” J. Di.. Equat., 20, 369–388 (1976).

    Google Scholar 

  20. O. Oleinik, “On the uniqueness of a generalized solution of the Cauchy problem for a nonlinear system of equations occurring in mechanics, ” Usp. Mat. Nauk, 12, 169–176 (1957).

    Google Scholar 

  21. N. H. Risebro, “A front-tracking alternative to the random choice method, ” Proc. Amer. Math. Soc., 117, 1125–1139 (1993).

    Google Scholar 

  22. B. L. Rozdesvenskii and N. Yanenko, Systems of Quasilinear Equations and Their Applications to Gas Dynamics. A.M.S. Translations of Mathematical Monographs, 55, Providence (1983).

  23. D. Serre, Systèmes de Lois de Conservation, Diderot Editeur (1996).

  24. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York (1983).

    Google Scholar 

  25. B. Temple, “Systems of conservation laws with invariant submanifolds, ” Trans. Amer. Math. Soc., 280, 781–795 (1983).

    Google Scholar 

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Bressan, A. Stability of Solutions to Hyperbolic Systems of Conservation Laws. Journal of Mathematical Sciences 104, 933–940 (2001). https://doi.org/10.1023/A:1009571007764

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