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

Abstract : 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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Submitted on : Friday, May 6, 2011 - 4:39:31 PM
Last modification on : Monday, May 11, 2020 - 6:14:04 PM
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François James, Nicolas Vauchelet. A remark on duality solutions for some weakly nonlinear scalar conservation laws. Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2011, 349, pp.657-661. ⟨10.1016/j.crma.2011.05.004⟩. ⟨hal-00591119⟩

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