Geodesic
Clausius theorem for hyperbolic scalar conservation laws
Novi Sad Journal of Mathematics, Tome 53 (2023) no. 1.

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I give for hyperbolic scalar conservation laws with non-linear flux, the ideas and the computations behind the definitions of entropic solution and kinetic solution in different cases (homogeneous, deterministic source terms, stochastic source terms): they derive from the Clausius theorem. In conclusion, I give the definitions for a stochastic source term which is a general Lévy noise.
Publié le :
DOI : 10.30755/NSJOM.10017
Classification : 60H15, 35-01, 35L65, 35L60, 35R60
Keywords: Hyperbolic scalar conservation laws, entropic solution, kinetic solution, stochastic source term, Lévy noise, Clausius theorem 
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Sylvain Dotti. Clausius theorem for hyperbolic scalar conservation laws. Novi Sad Journal of Mathematics, Tome 53 (2023) no. 1. doi : 10.30755/NSJOM.10017. http://geodesic.mathdoc.fr/articles/10.30755/NSJOM.10017/

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