Fractional BV solutions for 2×2 systems of conservation laws with a linearly degenerate field
Haspot, Boris; Junca, Stéphane (2020), Fractional BV solutions for 2×2 systems of conservation laws with a linearly degenerate field. https://basepub.dauphine.fr/handle/123456789/20611
TypeDocument de travail / Working paper
External document linkhttps://hal.archives-ouvertes.fr/hal-02532444
Cahier de recherche CEREMADE, Université Paris-Dauphine
MetadataShow full item record
CEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
Inria Sophia Antipolis - Méditerranée [CRISAM]
Laboratoire Jean Alexandre Dieudonné [JAD]
Abstract (EN)The class of 2×2 nonlinear hyperbolic systems with one genuinely nonlinear field and one linearly degenerate field are considered. Existence of global weak solutions for small initial data in fractional BV spaces BVs is proved. The exponent s is related to the usual fractional Sobolev derivative. Riemann invariants w and z corresponding respectively to the genuinely nonlinear component and to the linearly degenerate component play different key roles in this work. We obtain the existence of a global weak solution provided that the initial data written in Riemann coordinates (w0,z0) are small in BVs×L∞,1/3≤s<1. The restriction on the exponent s is due to a fundamental result of P.D. Lax, the variation of the Riemann invariant z on the Lax shock curve depends in a cubic way of the variation of the other Riemann invariant w.
Subjects / Keywordslinearly degenerate field
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