ON QUANTITATIVE COMPACTNESS ESTIMATES FOR HYPERBOLIC CONSERVATION LAWS

被引：0

作者：

Ancona, Fabio ^{[1
]}

Glass, Olivier ^{[2
]}

Nguyen, Khai T. ^{[3
]}

机构：

[1] Univ Padua, Dipartimento Matemat, Via Trieste 63, I-35121 Padua, Italy

[2] Univ Paris 09, CEREMADE, CNRS, UMR 7534, Pl Marechal Lattre de Tassigny, F-75775 Paris 16, France

[3] Penn State Univ, Dept Math, 235 McAllister Buiding, University Pk, PA 16802 USA

来源：

HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS | 2014年 / 8卷

关键词：

Hyperbolic equations; conservation laws; characteristics; compactness estimates; Kolmogorov entropy; SYSTEMS;

D O I：

暂无

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We are concerned with the compactness in L-loc(1) of the semigroup (S-t)(t >= 0) of entropy weak solutions generated by hyperbolic conservation laws in one space dimension. This note provides a survey of recent results establishing upper and lower estimates for the Kolmogorov epsilon-entropy of the image through the mapping S-t of bounded sets in L-1 boolean AND L-infinity, both in the case of scalar and of systems of conservation laws. As suggested by Lax [16], these quantitative compactness estimates could provide a measure of the order of "resolution" of the numerical methods implemented for these equations.

引用

页码：249 / 257

页数：9

共 50 条

[1] On compactness estimates for hyperbolic systems of conservation laws
Ancona, Fabio
Glass, Olivier
Nguyen, Khai T.
[J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2015, 32 (06): : 1229 - 1257
[2] Quantitative Compactness Estimates for Stochastic Conservation Laws
Karlsen, Kenneth H.
[J]. HYPERBOLIC PROBLEMS: THEORY, NUMERICS, APPLICATIONS, VOL I, HYP2022, 2024, 34 : 41 - 61
[3] 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
[4] A quantitative compactness estimate for scalar conservation laws
De Lellis, C
Golse, F
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2005, 58 (07) : 989 - 998
[5] Compactness estimates for difference schemes for conservation laws with discontinuous flux
Karlsen, Kenneth H.
Towers, John D.
[J]. IMA JOURNAL OF NUMERICAL ANALYSIS, 2024,
[6] A Posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws
Bressan, Alberto
Chiri, Maria Teresa
Shen, Wen
[J]. ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2021, 241 (01) : 357 - 402
[7] Stiff systems of hyperbolic conservation laws: Convergence and error estimates
Kurganov, A
Tadmor, E
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1997, 28 (06) : 1446 - 1456
[8] A Posteriori Error Estimates for Numerical Solutions to Hyperbolic Conservation Laws
Alberto Bressan
Maria Teresa Chiri
Wen Shen
[J]. Archive for Rational Mechanics and Analysis, 2021, 241 : 357 - 402
[9] ON KOLMOGOROV ENTROPY COMPACTNESS ESTIMATES FOR SCALAR CONSERVATION LAWS WITHOUT UNIFORM CONVEXITY
Ancona, Fabio
Glass, Olivier
Nguyen, Khai T.
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2019, 51 (04) : 3020 - 3051
[10] Hyperbolic Conservation Laws
Markfelder, Simon
[J]. CONVEX INTEGRATION APPLIED TO THE MULTI-DIMENSIONAL COMPRESSIBLE EULER EQUATIONS, 2021, 2294 : 13 - 25

← 1 2 3 4 5 →