*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 $L^1$.

For the most updated version and eventual errata see the page

http:/www.math.uzh.ch*index.php?id=publikationen&key1=493
*