# A quantitative compactness estimate for scalar conservation laws

created on 07 Jan 2004
modified by delellis on 03 May 2011

[BibTeX]

Published Paper

Inserted: 7 jan 2004
Last Updated: 3 may 2011

Journal: Comm. Pure Appl. Math.
Volume: 58
Number: 989--998
Year: 2004

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. 8 (1954) that the semigroup defining the entropy solution is compact in $L^1_{loc}$ for each positive time. The present note gives an estimate of the $\eps$-entropy in $L^1_{loc}$ of the set of entropy solutions at time $t>0$ whose initial data run through a bounded set in $L^1$.

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