De Lellis, C; Golse, F (2005). A quantitative compactness estimate for scalar conservation laws. Communications on Pure and Applied Mathematics, 58(7):989-998.
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.
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.
| Item Type: | Journal Article, refereed, original work |
|---|---|
| Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |
| Dewey Decimal Classification: | 510 Mathematics |
| Scopus Subject Areas: | Physical Sciences > General Mathematics
Physical Sciences > Applied Mathematics |
| Uncontrolled Keywords: | Applied Mathematics, General Mathematics |
| Language: | English |
| Date: | 2005 |
| Deposited On: | 05 Mar 2010 09:33 |
| Last Modified: | 28 Jun 2022 20:51 |
| 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 |
| OA Status: | Green |
| Publisher DOI: | https://doi.org/10.1002/cpa.20082 |
De Lellis, C