【摘 要】
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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.Th
【机 构】
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Fujian Province University Key Laboratory of Computational Science,School of Mathematical Sciences,H
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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.
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