Controlling conservation laws I: Entropy–entropy flux
Controlling conservation laws I: Entropy–entropy flux
复制标题
控制守恒定律 I：熵 — 熵通量
DOI：
10.1016/j.jcp.2023.112019
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发表时间：
2023
影响因子：
4.1
通讯作者：
Osher, Stanley
中科院分区：
文献类型：
--
作者：
Li, Wuchen;Liu, Siting;Osher, Stanley
研究了一类具有Lax熵-熵通量对的正则化守恒律的变分问题。首先引入了一个基于扩散守恒定律的修正最优输运空间。利用这个空间，我们证明了带有扩散的守恒律是“通量梯度流”。接下来，我们构造了这些流的变分问题，为此我们导出了正则化守恒律的对偶偏微分方程系统。给出了几个例子，包括交通流和汉堡方程。结合原始对偶算法和单调格式，我们成功地计算了守恒律的控制。
We study a class of variational problems for regularized conservation laws with Lax's entropy-entropy flux pairs. We first introduce a modified optimal transport space based on conservation laws with diffusion. Using this space, we demonstrate that conservation laws with diffusion are “flux–gradient flows”. We next construct variational problems for these flows, for which we derive dual PDE systems for regularized conservation laws. Several examples, including traffic flow and Burgers' equation, are presented. Incorporating both primal-dual algorithms and monotone schemes, we successfully compute the control of conservation laws.