Geodesic
A class of systems of quasilinear conservation laws
Sbornik. Mathematics, Tome 188 (1997) no. 5, pp. 725-751

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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. 
@article{SM_1997_188_5_a4,
     author = {E. Yu. Panov},
     title = {A class of systems of quasilinear conservation laws},
     journal = {Sbornik. Mathematics},
     pages = {725--751},
     publisher = {mathdoc},
     volume = {188},
     number = {5},
     year = {1997},
     language = {en},
     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/