Glasnik Matematicki, Vol. 55, No. 1 (2020), 101-111.

SCALAR CONSERVATION LAWS WITH CHARATHEODORY FLUX REVISITED

Nikola Konatar

Department of Natural Sciences and Mathematics, Faculty of Mathematics and Natural Sciences, University of Montenegro, Džordža Vašingtona bb, 81000 Podgorica, Crna Gora
e-mail: nikola.k@ucg.ac.me

Abstract.   We introduce a new approach for dealing with scalar conservation laws with the flux discontinuous with respect to the space variable and merely continuous with respect to the state variable which employs a variant of the kinetic formulation. We use it to improve results about the existence of solutions for non-degenerate scalar conservation laws with Caratheodory flux under a variant of non-degeneracy conditions.

2010 Mathematics Subject Classification.   35L65, 65M25

Key words and phrases.   Multidimensional scalar conservation law, discontinuous flux, existence, kinetic formulation, Caratheodory flux

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https://doi.org/10.3336/gm.55.1.09

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