Optimal contraception control for a nonlinear population model with size structure and a separable mortality

Rong  Liu; Feng-Qin  Zhang; Yuming Chen

doi:10.3934/dcdsb.2016112

Article Contents

2016, Volume 21, Issue 10: 3603-3618. Doi: 10.3934/dcdsb.2016112

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Optimal contraception control for a nonlinear population model with size structure and a separable mortality

1.
Department of Applied Mathematics, Yuncheng University, Yuncheng 044000
2.
Department of Applied Mathematics, Yuncheng University, Yuncheng, Shanxi 044000

Received: November 30, 2015

Revised: August 31, 2016

Published: November 2016

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Abstract

This paper is concerned with the problem of optimal contraception control for a nonlinear population model with size structure. First, the existence of separable solutions is established, which is crucial in obtaining the optimal control strategy. Moreover, it is shown that the population density depends continuously on control parameters. Then, the existence of an optimal control strategy is proved via compactness and extremal sequence. Finally, the conditions of the optimal strategy are derived by means of normal cones and adjoint systems.

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Mathematics Subject Classification: Primary: 49N90; Secondary: 92D25.

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