摘要
This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolutions of three biological species:prey,predator,and food for the prey or vegetation.The equation for the food density incorporates a hysteresis operator of generalized stop type accounting for underlying hysteresis effects occurring in the dynamical process.We study the problem of minimization of a given integral cost functional over solutions of the above system.The set-valued mapping defining the control constraint is state-dependent and its values are nonconvex as is the cost integrand as a function of the control variable.Some relaxationtype results for the minimization problem are obtained and the existence of a nearly optimal solution is established.
作者
陈斌
Sergey A.TIMOSHIN
Bin CHEN;Sergey A.TIMOSHIN(Fujian Province University Key Laboratory of Computational Science,School of Mathematical Sciences,Huaqiao University,Quanzhou 362021,China;Matrosov Institute for System Dynamics and Control Theory,Russian Academy of Sciences,Lermontov str,134,664033 Irkutsk,Russia)
基金
supported by National Natural Science Foundation of China(12071165 and 62076104)
Natural Science Foundation of Fujian Province(2020J01072)
Program for Innovative Research Team in Science and Technology in Fujian Province University,Quanzhou High-Level Talents Support Plan(2017ZT012)
Scientific Research Funds of Huaqiao University(605-50Y 19017,605-50Y14040)
supported by Ministry of Science and Higher Education of Russian Federation(075-15-2020-787,large scientific project"Fundamentals,methods and technologies for digital monitoring and forecasting of the environmental situation on the Baikal natural territory")。
