TY - JOUR
T1 - A nonlinear functional for general scalar hyperbolic conservation laws
AU - Liu, Hongxia
AU - Yang, Tong
PY - 2007/4/15
Y1 - 2007/4/15
N2 - 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.
AB - 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.
KW - General scalar conservation laws
KW - Generalized entropy functional
KW - Glimm's functional
KW - L1 estimates
UR - http://www.scopus.com/inward/record.url?scp=33847696040&partnerID=8YFLogxK
UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-33847696040&origin=recordpage
U2 - 10.1016/j.jde.2007.01.011
DO - 10.1016/j.jde.2007.01.011
M3 - RGC 21 - Publication in refereed journal
VL - 235
SP - 658
EP - 667
JO - Journal of Differential Equations
JF - Journal of Differential Equations
SN - 0022-0396
IS - 2
ER -