A note on the new glimm functional for general systems of hyperbolic conservation laws

Research output: Journal Publications and ReviewsRGC 21 - Publication in refereed journalpeer-review

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Original languageEnglish
Pages (from-to)815-842
Journal / PublicationMathematical Models and Methods in Applied Sciences
Volume20
Issue number5
Publication statusPublished - May 2010

Abstract

For systems of hyperbolic conservation laws, a new Glimm functional was recently constructed when the linearly degenerate manifold in each characteristic field is either the whole space or it consists of a finitely many smooth and transversal manifolds of codimension one. This new functional leads to the neat consistency and convergence rate estimation of the Glimm scheme. In this paper, by the motivation of the result in Ref. 2, we show that the corresponding new Glimm functional can be constructed for general systems only under the strict hyperbolic-AR assumption. © 2010 World Scientific Publishing Company.

Research Area(s)

  • Convergence rate, Glimm functionalGeneral conservation laws, Hyperbolicity