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Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2010

Existence result for the coupling problem of two scalar conservation laws with Riemann initial data

Résumé

This paper is devoted to the coupling problem of two scalar conservation laws through a fixed interface located for instance at x = 0. Each scalar conservation law is associated with its own (smooth) flux function and is posed on a half-space, namely x < 0 or x > 0. At interface x = 0 we impose a coupling condition whose objective is to enforce in a weak sense the continuity of a prescribed variable, which may differ from the conservative unknown (and the flux functions as well). We prove the existence of a solution to the coupled Riemann problem using a constructive approach. The latter allows in particular to highlight interesting features like non-uniqueness of both continuous and discontinuous (at interface x = 0) solutions. The behavior of some numerical scheme is also investigated.
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Dates et versions

hal-00871839 , version 1 (10-10-2013)

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Benjamin Boutin, Christophe Chalons, Pierre-Arnaud Raviart. Existence result for the coupling problem of two scalar conservation laws with Riemann initial data. Mathematical Models and Methods in Applied Sciences, 2010, 20 (10), pp.1859--1898. ⟨10.1142/S0218202510004817⟩. ⟨hal-00871839⟩
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