Kinetic formulation and uniqueness for scalar conservation laws with discontinuous flux
Graziano Crasta, Virginia De Cicco, Guido De Philippis
TL;DR
This paper establishes the uniqueness of BV solutions for scalar conservation laws with discontinuous flux in multiple dimensions, using kinetic solutions and analyzing entropy dissipation at flux discontinuities.
Contribution
It introduces a novel approach combining kinetic formulation with entropy analysis to prove uniqueness in complex multidimensional flux discontinuities.
Findings
Proves uniqueness of BV solutions in multiple dimensions.
Develops a kinetic solution framework for discontinuous flux.
Analyzes entropy dissipation along flux discontinuities.
Abstract
We prove a uniqueness result for BV solutions of scalar conservation laws with discontinuous flux in several space dimensions. The proof is based on the notion of kinetic solution and on a careful analysis of the entropy dissipation along the discontinuities of the flux.
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