Order preserving operators in problems of optimal control and in the theory of partial differential equations

(赋范)向量空间中的正性和序结构以及这些空间上的正性和保结构算子在算子理论及其应用中起着重要的作用，如动力系统和偏微分方程。在这个项目中，我们建议与来自莫斯科、Voronezh和Vladikavkaz的合作伙伴一起研究序空间中的最优控制问题，序结构和保序算子以及一般不是Riesz空间的偏序赋范空间上的算子半群。该项目建议书响应了关于DFG-RFBR合作的号召。该项目提案也是启动国际合作(2014年7月至2015年6月，与位于符拉迪卡夫卡兹的俄罗斯科学院成员合作)的延续。该项目提案的前一个版本已在2015年9月DFG-RSF合作框架内提交(GZ：CH 1282/3-1)，并得到了德国方面的积极评价，但没有得到俄罗斯方面的评价。我们仍然打算深化这一合作，并期望从这一国际合作中获得关于Pre-Riesz空间上的线性和非线性保序算子、这类算子的空间中的有限元以及序Banach空间上的正算子半群的新的见解和结果。

Positivity and order structures in (normed) vector spaces as well as positive and structure preserving operators on these spaces play an important role in operator theory and its applications such as dynamical systems and partial differential equations. In this project we propose to study, together with our partners from Moscow, Voronezh and Vladikavkaz, optimal control problems in ordered spaces, order structures and order preserving operators and semigroups of operators on partially ordered, normed spaces which are in general not Riesz spaces. This project proposal replies to a call about a DFG-RFBR Cooperation. This project proposal is also a continuation of an Initiation of an International Collaboration (from July 2014 to June 2015, together with members of the Russian Academy of Sciences at Vladikavkaz). A previous version of this project proposal has been submitted in the framework of a DFG-RSF Cooperation in September 2015 (GZ: CH 1282/3-1) and was evaluated positively on the German side, but not on the Russian side. We still intend to deepen this collaboration and expect from this international cooperation new insights and results for linear and nonlinear order preserving operators on pre-Riesz spaces, finite elements in spaces of such operators as well as for positive operator semigroups on ordered Banach spaces.