On compactness estimates for hyperbolic systems of conservation laws
On compactness estimates for hyperbolic systems of conservation laws
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关于守恒定律双曲系统的紧致性估计
DOI：
10.1016/j.anihpc.2014.09.002
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发表时间：
2014
影响因子：
1.9
通讯作者：
K. Nguyen
中科院分区：
文献类型：
--
作者：
F. Ancona;O. Glass;K. Nguyen
我们研究了半群映射（St）在1维空间中定义了守恒定律的一般双曲系统的熵弱解的L1轨迹上的紧性。我们通过L1∩L∞上有界集合的映射St，建立了图像的Kolmogorov ε-熵的下估计，该估计与作者建立的标量守恒律的下估计具有相同的1/ε阶。在具有真正非线性特征族的Temple系统中，我们也给出了这类集合的Kolmogorov ε-熵的1阶/ε的上估计，从而推广了De Lellis和Golse对具有凸通量的标量守恒律的同类估计。正如Lax所建议的那样，这些定量紧性估计可以提供对这些方程实施的数值方法的“分辨率”的度量。©2014 Elsevier Masson SAS版权所有。
We study the compactness in L1 loc of the semigroup mapping (St) t> 0 defining entropy weak solutions of general hyperbolic systems of conservation laws in one space dimension. We establish a lower estimate for the Kolmogorov ε-entropy of the image through the mapping St of bounded sets in L1∩ L∞, which is of the same order 1/ε as the ones established by the authors for scalar conservation laws. We also provide an upper estimate of order 1/ε for the Kolmogorov ε-entropy of such sets in the case of Temple systems with genuinely nonlinear characteristic families, that extends the same type of estimate derived by De Lellis and Golse for scalar conservation laws with convex flux. As suggested by Lax, these quantitative compactness estimates could provide a measure of the order of “resolution” of the numerical methods implemented for these equations.© 2014 Elsevier Masson SAS. All rights reserved.