REFERENCES
P. Baiti and H. K. Jenssen, “On the front tracking algorithm, ” J. Math. Anal. Appl. (in press).
A. Bressan, “Contractive metrics for nonlinear hyperbolic systems, ” Indiana Univ. Math. J., 37, 409–421 (1988).
A. Bressan, “Global solutions of systems of conservation laws by wave-front tracking, ” J. Math. Anal. Appl., 170, 414–432 (1992).
A. Bressan, “The unique limit of the Glimm scheme, ” Arch. Ration. Mech. Anal., 130, 205–230 (1995).
A. Bressan and R. M. Colombo, “The semigroup generated by 2×2 conservation laws, ” Arch. Ration. Mech. Anal., 133, 1–75 (1995)
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).
A. Bressan and P. Goatin, “Oleinik type estimates and uniqueness for n × n conservation laws, ” Preprint S.I.S.S.A., Trieste (1997).
A. Bressan and P. LeFloch, “Uniqueness of weak solutions to hyperbolic systems of conservation laws, ” Arch. Ration. Mech. Anal., 140, 301–317 (1997).
A. Bressan and M. Lewicka, “A uniqueness condition for hyperbolic systems of conservation laws, ” Preprint S.I.S.S.A., Trieste (1998).
A. Bressan, T. P. Liu and T. Yang, “L1 stability estimates for n×n conservation laws, ” Arch. Ration. Maech. Anal. (in press).
C. Dafermos, “Polygonal approximations of solutions of the initial value problem for a conservation law, ” J. Math. Anal. Appl., 38, 33–41 (1972).
R. J. DiPerna, “Global existence of solutions to nonlinear hyperbolic systems of conservation laws, ” J. Diff. Equat., 20, 187–212 (1976).
R. J. DiPerna, “Uniqueness of solutions to hyperbolic conservation laws, ” Indiana Univ. Math. J., 28, 137–188 (1979).
J. Glimm, “Solutions in the large for nonlinear hyperbolic systems of equations, ” Comm. Pure Appl. Math., 18, 697–715 (1965).
H. K. Jenssen, “Blowup for systems of conservation laws, ” Preprint (1998).
F. John, “Formation of singularities in one-dimensional nonlinear wave propagation, ” Comm. Pure Appl. Math., 27, 377–405 (1974).
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).
P. D. Lax, “Hyperbolic systems of conservation laws. II, ” Comm. Pure Appl. Math., 10, 537–566 (1957).
T. P. Liu, “Uniqueness of weak solutions of the Cauchy problem for general 2× 2 conservation laws, ” J. Di.. Equat., 20, 369–388 (1976).
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).
N. H. Risebro, “A front-tracking alternative to the random choice method, ” Proc. Amer. Math. Soc., 117, 1125–1139 (1993).
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).
D. Serre, Systèmes de Lois de Conservation, Diderot Editeur (1996).
J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, New York (1983).
B. Temple, “Systems of conservation laws with invariant submanifolds, ” Trans. Amer. Math. Soc., 280, 781–795 (1983).
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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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DOI: https://doi.org/10.1023/A:1009571007764