Lower compactness estimates for scalar balance laws
Lower compactness estimates for scalar balance laws
复制标题
标量平衡定律的较低紧凑性估计
DOI：
10.1002/cpa.21406
复制
发表时间：
2012
影响因子：
3
通讯作者：
K. Nguyen
中科院分区：
文献类型：
--
作者：
F. Ancona;O. Glass;K. Nguyen
本文研究了一维严格凸单量守恒律熵弱解半群（St）t≥0在Lloc 1中的紧性.对于t > 0的每一个，St的紧性由P. D.放松C给出了L1 n L∞到St中有界集的像的Kolmogorov e-熵的上估计。De Lellis和F.戈尔塞在这里，我们提供了与De Lellis和Golse建立的相同阶的e熵的较低估计，从而表明这样的e熵的大小为ε 1/ε。此外，我们将这些估计的紧性的情况下，凸平衡律。© 2012 Wiley Periodicals，Inc.
In this paper, we study the compactness in L loc1 of the semigroup (St)t≥0 of entropy weak solutions to strictly convex scalar conservation laws in one space dimension. The compactness of St for each t > 0 was established by P. D. Lax. Upper estimates for the Kolmogorov e‐entropy of the image of bounded sets in L1 n L∞ through St were given by C. De Lellis and F. Golse. Here we provide lower estimates on this e‐entropy of the same order as the one established by De Lellis and Golse, thus showing that such an e‐entropy is of size ≈ 1/ε. Moreover, we extend these estimates of compactness to the case of convex balance laws. © 2012 Wiley Periodicals, Inc.