This paper is devoted to studying two multiobjective problems for stochastic degenerate parabolic equations. The first one is a hierarchical control problem, in which the controls are classified into a pair of leaders and a pair of followers. For each pair of leaders, a Nash equilibrium is searched for a noncooperative game problem. The aim of the pair of leaders is to achieve null controllability of the system. The other multiobjective problem is an inverse initial problem under a Nash equilibrium strategy. In contrast to the classical inverse initial problem, an optimization problem for stochastic degenerate parabolic equations is first investigated. Then, the conditional stability of determining initial information is derived through terminal observation.  

　　Publication:  

　　SIAM Journal on Control and Optimization, Volume 61, Issue 4 (2023)  

　　http://dx.doi.org/10.1137/22M1510194  

　　Author:  

　　Yongyi Yu  

　　School of Mathematics, Jilin University, Changchun 130012, China.  

　　Ji-Feng Zhang  

　　Key Laboratory of Systems and Control, Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China, and School of Mathematics Sciences, University of Chinese Academy of Sciences, Beijing 100149, China.  

　　Email: jif@iss.ac.cn