A quantitative compactness estimate for scalar conservation laws

Camillo De Lellis; François Golse

doi:10.1002/cpa.20082

A quantitative compactness estimate for scalar conservation laws

Camillo De Lellis
, François Golse

Research output: Contribution to journal › Review article › peer-review

Abstract

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 ¹ for each positive time. The present note gives an estimate of the ε-entropy in L _loc ¹ of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L ¹.

Original language	English
Pages (from-to)	989-998
Number of pages	10
Journal	Communications on Pure and Applied Mathematics
Volume	58
Issue number	7
DOIs	https://doi.org/10.1002/cpa.20082
Publication status	Published - 1 Jul 2005
Externally published	Yes

Access to Document

10.1002/cpa.20082

Cite this

@article{30ff5ed786b3450bbe06c9f3a14b84c8,

title = "A quantitative compactness estimate for scalar conservation laws",

abstract = "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 1 for each positive time. The present note gives an estimate of the ε-entropy in L loc 1 of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L 1.",

author = "\{De Lellis\}, Camillo and Fran{\c c}ois Golse",

year = "2005",

month = jul,

day = "1",

doi = "10.1002/cpa.20082",

language = "English",

volume = "58",

pages = "989--998",

journal = "Communications on Pure and Applied Mathematics",

issn = "0010-3640",

number = "7",

}

TY - JOUR

T1 - A quantitative compactness estimate for scalar conservation laws

AU - De Lellis, Camillo

AU - Golse, François

PY - 2005/7/1

Y1 - 2005/7/1

N2 - 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 1 for each positive time. The present note gives an estimate of the ε-entropy in L loc 1 of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L 1.

AB - 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 1 for each positive time. The present note gives an estimate of the ε-entropy in L loc 1 of the set of entropy solutions at time t > 0 whose initial data run through a bounded set in L 1.

UR - https://www.scopus.com/pages/publications/20744455507

U2 - 10.1002/cpa.20082

DO - 10.1002/cpa.20082

M3 - Review article

AN - SCOPUS:20744455507

SN - 0010-3640

VL - 58

SP - 989

EP - 998

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

IS - 7

ER -

A quantitative compactness estimate for scalar conservation laws

Abstract

Access to Document

Other files and links

Fingerprint

Cite this