OPTIMAL CONTROL OF HARVESTING IN A PARABOLIC SYSTEM MODELING TWO SUBPOPULATIONS

2001 ◽  
Vol 11 (07) ◽  
pp. 1129-1141 ◽  
Author(s):  
SUZANNE M. LENHART ◽  
J. A. MONTERO
Keyword(s):  
Optimal Control ◽  
Differential System ◽  
Parabolic System ◽  
Existence And Uniqueness ◽  
System Modeling ◽  
Optimal Harvesting ◽  
Time Interval ◽  
Biological Parameters ◽  
Control Pair ◽  
Partial Differential System

An optimal harvesting problem for a parabolic partial differential system modeling two subpopulations of the same species is investigated. The two subpopulations are competing for resources. Under conditions on the smallness of the time interval and certain biological parameters, existence and uniqueness of an optimal control pair are established.

scholarly journals A nonlocal parabolic system with application to a thermoelastic problem

1999 ◽  
Vol 22 (4) ◽  
pp. 855-867
Author(s):  
Y. Lin ◽  
R. J. Tait
Keyword(s):  
Representation Theory ◽  
Parabolic System ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
System Modeling ◽  
Parabolic Systems ◽  
Thermoelastic Problem ◽  
Potential Representation

A system modeling the thermoelastic bards contacts is studied. The problem is first transformed into an equivalent nonlocal parabolic systems using a transformation, and then the existence and uniqueness of the solutions are demonstrated via the theoretical potential representation theory of the parabolic equations. Finally some realistic situations in the applications are discussed using the results obtained in this paper.

OPTIMAL HARVESTING PROBLEM FOR AN AGE-DEPENDENT n-DIMENSIONAL COMPETING SYSTEM WITH DIFFUSION

2008 ◽  
Vol 01 (02) ◽  
pp. 133-145 ◽  
Author(s):  
ZHIXUE LUO ◽  
ZE-RONG HE
Keyword(s):  
Optimal Control ◽  
Control Strategy ◽  
Existence And Uniqueness ◽  
Spatial Diffusion ◽  
Optimal Harvesting ◽  
Negative Solution ◽  
Optimal Control Strategy ◽  
Age Dependent ◽  
The Fixed Point Theorem ◽  
Existence Of Optimal Control

In this work, optimal harvesting policy for an age-dependent and spatial diffusion n-dimensional competing species is discussed. The existence and uniqueness of non-negative solution to the system are investigated by using the fixed point theorem. The existence of optimal control strategy is discussed and optimality conditions are obtained. Our results extend some known criteria.

OPTIMAL CONTROL FOR A PREDATOR-PREY SYSTEM WITH AGE-DEPENDENT

2009 ◽  
Vol 02 (01) ◽  
pp. 45-59 ◽  
Author(s):  
ZHIXUE LU
Keyword(s):  
Optimal Control ◽  
Existence And Uniqueness ◽  
Normal Cone ◽  
Optimal Harvesting ◽  
Negative Solution ◽  
Optimal Control Strategy ◽  
Predator Prey ◽  
Prey System ◽  
Age Dependent ◽  
Existence Of Optimal Control

This paper is concerned with optimal harvesting policy for predator-prey system of three species with age-dependent. The existence and uniqueness of non-negative solution of the system are proved using the fixed pint theorem. The existence of optimal control strategy is discussed, optimality conditions are derived by means of normal cone and Dubovitskii–Milyutin's general theory. Our results extend some known criteria.

scholarly journals Global existence and asymptotic behaviour of solutions for a hyperbolic-parabolic model of chemotaxis on network

2021 ◽  
Author(s):  
Yafeng Li ◽  
Chunlai Mu ◽  
Xin Qiao
Keyword(s):  
Global Existence ◽  
Asymptotic Behaviour ◽  
Parabolic System ◽  
Existence And Uniqueness ◽  
System Modeling ◽  
Global Solutions ◽  
Energy Estimates ◽  
Parabolic Model ◽  
Biological Phenomena ◽  
Acyclic Network

In this paper, we discuss a hyperbolic-parabolic system modeling biological phenomena evolving on a network. The global existence of the is obtained by using energy estimates with suitable the transmission conditions at interior. Moreover, for the case of acyclic network, the existence and uniqueness of stationary solution to the system is proposed and it is proved that these ones are asymptotic profiles for a class of global solutions

scholarly journals Optimal Control and Positional Controllability in a One-Sector Economy

Games ◽  
2021 ◽  
Vol 12 (1) ◽  
pp. 11
Author(s):  
Nikolai Grigorenko ◽  
Lilia Luk’yanova
Keyword(s):  
Optimal Control ◽  
Production Capacity ◽  
Quality Criterion ◽  
Zero Order ◽  
Suboptimal Control ◽  
Time Interval ◽  
Bounded Control ◽  
Optimal Value ◽  
Current Production ◽  
The Given

A model of production funds acquisition, which includes two differential links of the zero order and two series-connected inertial links, is considered in a one-sector economy. Zero-order differential links correspond to the equations of the Ramsey model. These equations contain scalar bounded control, which determines the distribution of the available funds into two parts: investment and consumption. Two series-connected inertial links describe the dynamics of the changes in the volume of the actual production at the current production capacity. For the considered control system, the problem is posed to maximize the average consumption value over a given time interval. The properties of optimal control are analytically established using the Pontryagin maximum principle. The cases are highlighted when such control is a bang-bang, as well as the cases when, along with bang-bang (non-singular) portions, control can contain a singular arc. At the same time, concatenation of singular and non-singular portions is carried out using chattering. A bang-bang suboptimal control is presented, which is close to the optimal one according to the given quality criterion. A positional terminal control is proposed for the first approximation when a suboptimal control with a given deviation of the objective function from the optimal value is numerically found. The obtained results are confirmed by the corresponding numerical calculations.

scholarly journals Optimal control of a viscous generalized θ-type dispersive equation with weak dissipation

2020 ◽  
Vol 18 (1) ◽  
pp. 1302-1316
Author(s):  
Guobing Fan ◽  
Zhifeng Yang
Keyword(s):  
Boundary Condition ◽  
Optimal Control ◽  
Weak Solution ◽  
Existence And Uniqueness ◽  
Optimal Solution ◽  
Dispersive Equation ◽  
Weak Dissipation ◽  
Formula Type

Abstract In this paper, we investigate the problem for optimal control of a viscous generalized \theta -type dispersive equation (VG \theta -type DE) with weak dissipation. First, we prove the existence and uniqueness of weak solution to the equation. Then, we present the optimal control of a VG \theta -type DE with weak dissipation under boundary condition and prove the existence of optimal solution to the problem.

scholarly journals On the differential system govering flows in magnetic field with data inLp

1998 ◽  
Vol 21 (2) ◽  
pp. 299-305 ◽  
Author(s):  
Fengxin Chen ◽  
Ping Wang ◽  
Chaoshun Qu
Keyword(s):  
Magnetic Field ◽  
Initial Data ◽  
Boundary Conditions ◽  
Differential System ◽  
Existence And Uniqueness ◽  
Mhd Equations ◽  
The Earth ◽  
Initial And Boundary Conditions ◽  
Time Existence ◽  
The Magnetic Field

In this paper we study the system governing flows in the magnetic field within the earth. The system is similar to the magnetohydrodynamic (MHD) equations. For initial data in spaceLp, we obtained the local in time existence and uniqueness ofweak solutions of the system subject to appropriate initial and boundary conditions.

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