A nonlinear functional for general scalar hyperbolic conservation laws

Hongxia Liu; Tong Yang

doi:10.1016/j.jde.2007.01.011

Author(s)

Hongxia Liu
Tong Yang

Related Research Unit(s)

Department of Mathematics

Detail(s)

Original language	English
Pages (from-to)	658-667
Journal / Publication	Journal of Differential Equations
Volume	235
Issue number	2
Publication status	Published - 15 Apr 2007

Link(s)

DOI	DOI https://doi.org/10.1016/j.jde.2007.01.011 Final Published version
	Check@CityULib
Link to Scopus	https://www.scopus.com/record/display.uri?eid=2-s2.0-33847696040&origin=recordpage
Permanent Link	https://scholars.cityu.edu.hk/en/publications/publication(90363063-3196-4bda-b714-064558b13c86).html

Abstract

A generalized entropy functional was introduced in [T.-P. Liu, T. Yang, A new entropy functional for scalar conservation laws, Comm. Pure Appl. Math. 52 (1999) 1427-1442] for the scalar hyperbolic conservation laws with convex flux function. This functional was crucially used in the functional approach to the L¹ stability study on the system of hyperbolic conservation laws when each characteristic field is either genuinely nonlinear or linearly degenerate. However, how to construct the generalized entropy functional for scalar conservation laws with general flux, and then how to apply the functional approach to the L¹ study on general systems are still open. In this paper, we construct a new nonlinear functional which gives some partial answer to this question and we expect the analysis will shed some light on the future investigation in this direction. © 2007 Elsevier Inc. All rights reserved.