Geodesic
On the sign of Colombeau functions and applications to conservation laws
Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 245-264

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A generalized concept of sign is introduced in the context of Colombeau algebras. It extends the sign of the point-value in the case of sufficiently regular functions. This concept of generalized sign is then used to characterize the entropy condition for discontinuous solutions of scalar conservation laws.
Classification : 35L67, 46F30
Keywords: Colombeau algebra; generalized sign; conservation law; entropy condition 
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Jelínek, Jiří; Pražák, Dalibor. On the sign of Colombeau functions and applications to conservation laws. Commentationes Mathematicae Universitatis Carolinae, Tome 50 (2009) no. 2, pp. 245-264. http://geodesic.mathdoc.fr/item/CMUC_2009__50_2_a5/