具有间断通量的标量守恒律的精确与最优能控性
偏微分方程分析
2020-09-29 v1
摘要
本文描述了具有间断通量的标量守恒律的可达集，并解决了一个最优控制问题。我们给出了可达集的充要条件。为获得可达集，描述了一种新的反向求解方法。关于最优控制问题，我们首先证明极小元的存在性，然后反向算法使我们能够计算它。同一方法也适用于计算精确控制问题的初值数据控制。我们的证明方法依赖于具有间断通量的守恒律的显式公式以及特征曲线的更精细性质。
引用
@article{arxiv.2009.13324,
title = {Exact and optimal controllability for scalar conservation laws with discontinuous flux},
author = {Adimurthi and Shyam Sundar Ghoshal},
journal= {arXiv preprint arXiv:2009.13324},
year = {2020}
}
备注
It is to be noted most of the ideas and technical details was in the arxiv version arXiv:1603.01473 but that there was a gap in the proof, because the reflected characteristics was not being considered and hence the definition of the reachable set was incomplete. In this present version we fill this gap in subsection 3.3 and present a modified version