A Bhatnagar-Gross-Krook approximation to scalar conservation laws with discontinuous flux

Florent Berthelin (1) , Julien Vovelle (2)

1 JAD - Laboratoire Jean Alexandre Dieudonné
2 ICJ - Institut Camille Jordan

We study the BGK approximation to first-order scalar conservation laws with a flux which is discontinuous in the space variable. We show that the Cauchy Problem for the BGK approximation is well-posed and that, as the relaxation parameter tends to 0, it converges to the (entropy) solution of the limit problem.

Domaines: Equations aux dérivées partielles [math.AP]

Florent Berthelin, Julien Vovelle. A Bhatnagar-Gross-Krook approximation to scalar conservation laws with discontinuous flux. Proceedings of the Royal Society of Edinburgh: Section A, Mathematics, 2010, 140 (5), pp.953 -- 972. ⟨10.1017/S030821050900105X⟩. ⟨hal-00951469⟩