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A quantitative compactness estimate for scalar conservation laws


De Lellis, C; Golse, F (2005). A quantitative compactness estimate for scalar conservation laws. Communications on Pure and Applied Mathematics, 58(7):989-998.

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 > 0 whose initial data run through a bounded set in L1. © 2005 Wiley Periodicals, Inc.

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 > 0 whose initial data run through a bounded set in L1. © 2005 Wiley Periodicals, Inc.

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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:2005
Deposited On:05 Mar 2010 09:33
Last Modified:06 Dec 2017 20:47
Publisher:Wiley-Blackwell
ISSN:0010-3640
Additional Information:This is a preprint of an article accepted for publication in [Communications on Pure and Applied Mathematics] © copyright 2005 John Wiley & Sons
Publisher DOI:https://doi.org/10.1002/cpa.20082

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