Geodesic
A class of systems of quasilinear conservation laws
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 725-751 
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/
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     author = {E. Yu. Panov},
     title = {A class of systems of quasilinear conservation laws},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1997_188_5_a4/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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