Geodesic
On $2\times 2$ systems of conservation laws with fluxes that are entropies
Electronic Journal of Differential Equations, Tome 2003 (2003).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: In this article, we study systems of conservation laws with two dependent and two independent variables which have the property that the fluxes are entropies. Several characterizations of such flux functions are presented. It turns out, that the corresponding systems automatically possess a large class of additional entropies, they are closely related to a kinetic equation, and, in the case of strict hyperbolicity, they can be decoupled into two independent Burgers' equations. The isentropic Euler equations with zero or cubic pressure laws are the most prominent examples of such systems, but other examples are also presented.
Classification : 35L65, 82C40
Keywords: nonlinear conservation laws, entropies 
@article{EJDE_2003__2003__a174,
     author = {Junk, Michael},
     title = {On $2\times 2$ systems of conservation laws with fluxes that are entropies},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2003},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a174/}
}
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Junk, Michael. On $2\times 2$ systems of conservation laws with fluxes that are entropies. Electronic Journal of Differential Equations, Tome 2003 (2003). http://geodesic.mathdoc.fr/item/EJDE_2003__2003__a174/