A remark on duality solutions for some weakly nonlinear scalar conservation laws

Details A remark on duality solutions for some weakly nonlinear scalar conservation laws A remark on duality solutions for some weakly nonlinear scalar conservation laws

2011-05-06

arxiv.org/abs/1105.1308v1

Comptes Rendus de l Acad\'emie des Sciences - Series I - Mathematics 349 (2011) 657-661

Mathematics

Analysis of PDEs

Scientific paper

10.1016/j.crma.2011.05.004

We investigate existence and uniqueness of duality solutions for a scalar conservation law with a nonlocal interaction kernel. Following the work of Bouchut and James (Comm. Partial Diff. Eq., 24, 1999), a notion of duality solution for such a nonlinear system is proposed, for which we do not have uniqueness. Then we prove that a natural definition of the flux allows to select a solution for which uniqueness holds.

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