On the theory of generalized entropy solutions of the Cauchy problem for a class of non-strictly hyperbolic systems of conservation laws

Sbornik Mathematics

Volumn 191, Issue 1-2, 2000, Pages 121-150

  Panov, E Yu ^a  

^a NONE

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EID: 0034341443     PISSN: 10645616     EISSN: 14684802     Source Type: Journal    
DOI: 10.1070/SM2000v191n01ABEH000450     Document Type: Article

References (26)

1. E. Yu. Panov, "A class of systems of quasilinear conservation laws", Mat. Sb. 188:5 (1997), 85-112; English transl. in Sb. Math. 188 (1997).
2. E. Yu. Panov, "A class of systems of quasilinear conservation laws", Mat. Sb. 188:5 (1997), 85-112; English transl. in Sb. Math. 188 (1997).
3. E. Yu. Panov, "On the non-local theory of generalized entropy solutions of the Cauchy problem for a class of hyperbolic conservation laws", Izv. Ross. Akad. Nauk Ser. Mat. 63:1 (1999), 133-184; English transl. in Izv. Math. 63 (1999).
4. E. Yu. Panov, "On the non-local theory of generalized entropy solutions of the Cauchy problem for a class of hyperbolic conservation laws", Izv. Ross. Akad. Nauk Ser. Mat. 63:1 (1999), 133-184; English transl. in Izv. Math. 63 (1999).
5. B.L. Rozdestvenskii [Rozhdestvenskiǐ] and N. N. Janenko [Yanenko], Systems of quasilinear equations and their applications to gas dynamics, Nauka, Moscow 1978; English transl., Amer. Math. Soc., Providence, RI 1983.
6. B.L. Rozdestvenskii [Rozhdestvenskiǐ] and N. N. Janenko [Yanenko], Systems of quasilinear equations and their applications to gas dynamics, Nauka, Moscow 1978; English transl., Amer. Math. Soc., Providence, RI 1983.
7. P. D. Lax, "Hyperbolic systems of conservation laws", Comm. Partial Differential Equations 10 (1957), 537-566.
8. S.N. Kruzhkov, "First-order quasilinear equations in several independent variables", Mat. Sb. 81:2 (1970), 228-255; English transl. in Math. USSR-Sb. 10 (1970).
9. S.N. Kruzhkov, "First-order quasilinear equations in several independent variables", Mat. Sb. 81:2 (1970), 228-255; English transl. in Math. USSR-Sb. 10 (1970).
10. P.D. Lax, "Shock waves and entropy", Shock waves and entropy, contributions to nonlinear functional analysis, Academic Press, New York 1971, pp. 603-634.
11. M. Hirsch, Differential topology, Springer-Verlag, New York 1976.
12. S. N. Kruzhkov and E. Yu. Panov, "Osgood's type conditions for uniqueness of entropy solutions to Cauchy problem for quasilinear conservation laws of the first order", Ann. Univ. Ferrara Sez. VII (N.S.) 15 (1994), 31-53.
13. Ph. Benilan and S. N. Kruzhkov, "First-order quasilinear equations with continuous nonlinearities", Dokl. Akad. Nauk 339:2 (1994), 151-154; English transl. in Russian Acad. Sci. Dokl. Math. 50 (1995).
14. Ph. Benilan and S. N. Kruzhkov, "First-order quasilinear equations with continuous nonlinearities", Dokl. Akad. Nauk 339:2 (1994), 151-154; English transl. in Russian Acad. Sci. Dokl. Math. 50 (1995).
15. Ph. Benilan and S. N. Kruzhkov, "Conservation laws with continuous flux functions", Nonlinear Differential Equations Appl. 3 (1996), 395-419.
16. E. Yu. Panov, "On measure-valued solutions of the Cauchy problem for a first-order quasilinear equation", Izv. Ross. Akad. Nauk Ser. Mat. 60:2 (1996), 107-148; English transl. in Izv. Math. 60 (1996).
17. E. Yu. Panov, "On measure-valued solutions of the Cauchy problem for a first-order quasilinear equation", Izv. Ross. Akad. Nauk Ser. Mat. 60:2 (1996), 107-148; English transl. in Izv. Math. 60 (1996).
18. S. N. Kruzhkov and E. Yu. Panov, "First-order conservative quasilinear laws with an infinite domain of dependence on the initial data", Dokl. Akad. Nauk SSSR 314:1 (1990), 79-84; English transl. in Soviet Math. Dokl. 42 (1991).
19. S. N. Kruzhkov and E. Yu. Panov, "First-order conservative quasilinear laws with an infinite domain of dependence on the initial data", Dokl. Akad. Nauk SSSR 314:1 (1990), 79-84; English transl. in Soviet Math. Dokl. 42 (1991).
20. S. D. Eidel'man, Parabolic systems, Nauka, Moscow 1964; English transl., North-Holland, Amsterdam 1969.
21. L. Tartar, "Compensated compactness and applications to partial differential equations", Research notes in mathematics, nonlinear analysis, and mechanics, Heriot-Watt Symposium, vol. 4, 1979, pp. 136-212.
22. R. J. DiPerna, "Measure-valued solutions to conservation laws", Arch. Rational Mech. Anal. 88 (1985), 223-270.
23. J. Berg and J. Löfström, Interpolation spaces. An introduction, Springer-Verlag, Berlin 1976.
24. F. Murat, "Compacité par compensation", Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 5 (1978), 489-507.
25. E. Yu. Panov, "On strong precompactness of bounded sets of measure-valued solutions of a first-order quasilinear equation", Mat. Sb. 186:5 (1995), 103-114; English transl. in Sb. Math. 186 (1995).
26. E. Yu. Panov, "On strong precompactness of bounded sets of measure-valued solutions of a first-order quasilinear equation", Mat. Sb. 186:5 (1995), 103-114; English transl. in Sb. Math. 186 (1995).