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Preprint 2009-044

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

Jiale Hua and Tong Yang

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 co-dimension 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 [1], we show that the corresponding new Glimm functional can be constructed for general systems only under the strict hyperbolicity assumption.

[1] S.Bianchini, Interaction estimates and Glimm functional for general hyperbolic systems, Discrete Contin. Dyn. Syst., 9 (2003), pp.133–166.

Paper:
Available as PDF (352 Kbytes).
Author(s):
Jiale Hua,
Tong Yang,
Publishing information:
Comments:
Updated 2009-09-06 and 2009-11-10.
Submitted by:
; 2009-08-12.