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

Izvestiya Mathematics

Volumn 63, Issue 1, 1999, Pages 133-179

  Panov, E Yu ^a  

^a LOBACHEVSKY STATE UNIVERSITY OF NIZHNY NOVGOROD   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001993940     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/im1999v063n01abeh000232     Document Type: Article

References (17)

1. I. M. Glazman and Yu. I. Lyubich, Finite-dimensional linear analysis, Nauka, Moscow 1969. (Russian)
2. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of quasilinear equations and their applications to gas dynamics. Mir, Moscow 1978; English transl., American Mathematical Society, Providence, Rhode Island 1983.
3. S. N. Kruzhkov, "Quasilinear first-order equations in several independent variables", Mat. Sbornik 81 (1970), 228-255; English transl. in Math. USSR-Sb. 10 (1970).
4. P. D. Lax, Shock waves and entropy, contributions to Nonlinear Functional Analysis (E. A. Zarantonello, ed.), Academic Press, New York-London 1971, pp. 603-634.
5. M. W. Hirsch, Differential topology. Springer-Verlag, New York-Heidelberg-Berlin 1976; Russian transl., Mir, Moscow 1979.
6. xx" Comm. Pure Appl. Math. 3:3 (1950), 201-230.
7. S. N. Kruzhkov and E. Yu. Panov, "Conservative quasilinear first-order laws with an infinite domain of dependence on the initial data", Dokl. Akad. Nauk SSSR 314 (1990), 79-84; English transl., Soviet Math. Dokl. 42 (1991), 316-321.
8. 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", Annali Univ. Ferrara-Sez. 15 (1994), 31-53.
9. 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., Math. Izv. 60 (1996), 335-377.
10. P. Benilan and S. N. Kruzhkov, "Quasilinear, first-order equations with continuous nonlinearities", Ross. Akad. Nauk Dokl. 339 (1994), 151-154; English transl., Russian Acad. Sci. Dokl. Math. 50 (1995), 391-396.
11. E. Yu. Panov, "A class of systems of quasilinear conservation laws", Mat. Sbornik 188 (1997), 85-112; English transl., Sb. Math. 188 (1997), 725-751.
12. E. Yu. Panov, "Generalized solutions of the Cauchy problem for some classes of first order hyperbolic systems", Vestnik Moskov. Univ. Ser. 1 Mat. Mekh. 1996, no. 6, 75-77; English transl. in Moscow Univ. Math. Bull. 51 (1996).
13. S. D. Eidel'man, Parabolic systems, North-Holland, Amsterdam-London 1969; Russian transl., Mir, Moscow 1979.
14. 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.
15. R. J. DiPerna, "Measure-valued solutions to conservation laws", Arch. Rational Mech. Anal. 88 (1985), 223-270.
16. J. Bergh and J. Loefstroem, Interpolation spaces. An introduction, Springer-Verlag, Berlin-Heidelberg-New York 1976; Russian transl., Mir, Moscow 1980.
17. F. Murat, "Compacité par compensation", Ann. Scuola Norm. Sup. Pisa 5 (1978), 489-507.