TitleA quantitative compactness estimate for scalar conservation laws.
Publication TypeJournal Article
Year of Publication2005
AuthorsDe Lellis C., Golse F.
JournalCommunications on Pure and Applied Mathematics
Volume58
Pagination989–998
PublisherWiley-Blackwell
Type of Articlescalar
ISSN0010-3640
KeywordsApplied Mathematics, General Mathematics
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 for each positive time. The present note gives an estimate of the -entropy in L of the set of entropy solutions at time t \ensuremath> 0 whose initial data run through a bounded set in L1. \copyright 2005 Wiley Periodicals, Inc.

Notes

Comm. Pure Appl. Math. 58 (2005), no. 7, 989–998.

URLhttp://onlinelibrary.wiley.com/doi/10.1002/cpa.20082/abstract;jsessionid=9C41677BAABD402F02E61E46EBDC67F8.d03t01
DOI10.1002/cpa.20082
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