This paper addresses a nonlinear partial differential control system arising in population dynamics.The system consist of three diffusion equations describing the evolu-tions 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 ac-counting 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 relaxation-type results for the minimization problem are obtained and the existence of a nearly optimal solution is established.

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

数学物理学报（英文版）

[1]Bin CHEN;Sergey A.TIMOSHIN-.OPTIMAL CONTROL OF A POPULATION DYNAMICS MODEL WITH HYSTERESIS)[J].数学物理学报（英文版）,2022(01):283-298

OPTIMAL,POPULATION,HYSTERESIS,integrand

CONTROL,OF,DYNAMICS,MODEL,WITH,This,paper,addresses,nonlinear,partial,differential,control,system,arising,population,dynamics,consist,three,diffusion,equations,describing,evolu,biological,species,prey,predator,food,vegetation,density,incorporates,hysteresis,operator,generalized,stop,type,ac,counting,underlying,effects,occurring,dynamical,process,We,study,problem,minimization,given,integral,cost,functional,over,solutions,above,set,valued,mapping,defining,constraint,state,dependent,its,values,are,nonconvex,as,variable,Some,relaxation,results,obtained,existence,nearly,optimal,established

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