Geodesic
A class of systems of quasilinear conservation laws
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 725-751 Cet article a éte moissonné depuis la source Math-Net.Ru

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Hyperbolic systems of conservation laws with a functional-calculus operator on the right-hand side are considered in the space of second-order symmetric matrices. The entropies of such systems are described. The concept of a generalized entropy solution (g.e.s.) of the corresponding Cauchy problem is introduced, the properties of g.e.s.'s are analyzed, and the lack of their uniqueness in the general case is demonstrated. Using a stronger version of the defining entropy condition, the class of strong g.e.s.'s is distinguished. The Cauchy problem under discussion is shown to be uniquely soluble in this class. 
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     author = {E. Yu. Panov},
     title = {A class of systems of quasilinear conservation laws},
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     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_5_a4/}
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E. Yu. Panov. A class of systems of quasilinear conservation laws. Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 725-751. http://geodesic.mathdoc.fr/item/SM_1997_188_5_a4/

[1] Glazman I. M., Lyubich Yu. I., Konechnomernyi lineinyi analiz, Nauka, M., 1969 | MR | Zbl

[2] Rozhdestvenskii B. L., Yanenko N. N., Sistemy kvazilineinykh uravnenii i ikh prilozheniya k gazovoi dinamike, Nauka, M., 1978 | MR | Zbl

[3] Kruzhkov S. N., “Kvazilineinye uravneniya pervogo poryadka so mnogimi nezavisimymi peremennymi”, Matem. sb., 81:2 (1970), 228–255 | MR | Zbl

[4] Lax P. D., “Shock waves and entropy”, Shock waves and entropy, contributions to Nonlinear Functional Analysis, ed. E. A. Zarantonello, Academic Press, New York, 1971, 603–634 | MR

[5] Kruzhkov S. N., Panov E. Yu., “Konservativnye kvazilineinye zakony pervogo poryadka s beskonechnoi oblastyu zavisimosti ot nachalnykh dannykh”, Dokl. AN SSSR, 314:1 (1990), 79–84 | MR | Zbl

[6] Panov E. Yu., Obobschennye resheniya zadachi Koshi dlya kvazilineinykh zakonov sokhraneniya, Diss. $\dots$ kand. fiz.-matem. nauk, MGU, M., 1991

[7] Benilan F., Kruzhkov S. N., “Kvazilineinye uravneniya pervogo poryadka s nepreryvnymi nelineinostyami”, Dokl. AN, 339:2 (1994), 151–154 | MR | Zbl

[8] Tartar L., “Compensated compactness and applications to partial differential equations”, Research notes in mathematics, nonlinear analysis, and mechanics, Heriot-Watt Symposium, 1979, 136–212 | MR | Zbl

[9] DiPerna R. J., “Generalized solutions to conservation laws, in system of nonlinear partial differential equations”, NATO ASI Series, ed. J. M. Ball, D. Reidel Pub. Co., 1983

[10] Panov E. Yu., “Silnye meroznachnye resheniya zadachi Koshi dlya kvazilineinogo uravneniya pervogo poryadka s ogranichennoi meroznachnoi nachalnoi funktsiei”, Vestn. MGU. Ser. 1, matem., mekh., 1993, no. 1, 20–23 | MR | Zbl

[11] Panov E. Yu., “O meroznachnykh resheniyakh zadachi Koshi dlya kvazilineinogo uravneniya pervogo poryadka”, Izv. RAN. Ser. matem., 60:2 (1996), 107–148 | MR | Zbl