A quantitative compactness estimate for scalar conservation laws

被引：13

作者：

De Lellis, C ^{[1
]}

Golse, F

机构：

[1] ETH Zentrum, Dept Math, CH-8092 Zurich, Switzerland

[2] Lab JL Lions, F-75252 Paris, France

来源：

COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS | 2005年 / 58卷 / 07期

关键词：

D O I：

10.1002/cpa.20082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the case of a scalar conservation law with convex flux in space dimension one., P. D. Lax proved [Comm. Pure and Appl. Math. 7 (1954)] that the semigroup defining the entropy solution is compact in L-loc(l) for each positive time. The present note gives an estimate of the E-entropy in L-loc(l) of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L-1. (c) 2005 Wiley Periodicals, Inc.

引用

页码：989 / 998

页数：10

共 50 条

[31] Γ -Entropy Cost for Scalar Conservation Laws
Giovanni Bellettini
Lorenzo Bertini
Mauro Mariani
Matteo Novaga
[J]. Archive for Rational Mechanics and Analysis, 2010, 195 : 261 - 309
[32] ON THE CONCENTRATION OF ENTROPY FOR SCALAR CONSERVATION LAWS
Bianchini, Stefano
Marconi, Elio
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, 2016, 9 (01): : 73 - 88
[33] Scalar conservation laws with stochastic forcing
Debussche, A.
Vovelle, J.
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2010, 259 (04) : 1014 - 1042
[34] A priori error estimate for a well-balanced scheme designed for inhomogeneous scalar conservation laws
Gosse, L
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1998, 327 (05): : 467 - 472
[35] On compactness of bounded solutions to multidimensional conservation laws with memory
Eduard Feireisl
Hana Petzeltová
[J]. Nonlinear Differential Equations and Applications NoDEA, 1998, 5 : 193 - 204
[36] COMPENSATED COMPACTNESS AND GENERAL SYSTEMS OF CONSERVATION-LAWS
DIPERNA, RJ
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1985, 292 (02) : 383 - 420
[37] Compensated compactness for 2D conservation laws
Tadmor, E
Rascle, M
Bagnerini, P
[J]. JOURNAL OF HYPERBOLIC DIFFERENTIAL EQUATIONS, 2005, 2 (03) : 697 - 712
[38] COMPENSATED COMPACTNESS AND HYPERBOLIC SYSTEMS OF CONSERVATION-LAWS
SERRE, D
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1984, 299 (12): : 555 - 558
[39] On compactness of bounded solutions to multidimensional conservation laws with memory
Feireisl, Eduard
Petzeltova, Hana
[J]. NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS, 1998, 5 (02): : 193 - 204
[40] A theory of implicit methods for scalar conservation laws
Breuss, M
[J]. HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, 2003, : 377 - 386

← 1 2 3 4 5 →