论文标题
非局部相互作用方程的最佳控制问题
Optimal control problems of nonlocal interaction equations
论文作者
论文摘要
在目前的工作中，我们处理的解决方案存在与传输方程相关的最佳控制问题。个人人群的行为将受到控制剂的存在的影响，其作用是将个体的动态带入特定目标。个体人口的动力学是通过合适的非局部运输方程来描述的，而代理群体的作用是由最佳控制问题设计的。该模型首先在[12]中研究了一类连续的非本地电位，而在本项目中，我们考虑了目标传输方程的梯度流式公式中的轻度奇异电位的情况。
In the present work we deal with the existence of solutions for optimal control problems associated to transport equations. The behaviour of a population of individuals will be influenced by the presence of a population of control agents whose role is to lead the dynamics of the individuals towards a specific goal. The dynamics of the population of individuals is described by a suitable nonlocal transport equation, while the role of the population of agents is designed by the optimal control problem. This model has been first studied in [12] for a class of continuous nonlocal potentials, while in the present project we consider the case of mildly singular potentials in a gradient flow formulation of the target transport equation.
