Global existence and uniqueness of positive solutions and optimal control for a novel model of pest control |
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| Authors: | Huili Xiang |
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| Affiliation: | 1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei, P.R. China;2. Department of Mathematics, Hubei University for Nationalities, Enshi, Hubei, P.R. China |
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| Abstract: | In the present paper, a novel model of pest control governed by coupled sets of partial and ordinary differential equations is investigated in detail. Global existence and uniqueness of positive solutions to the above model are obtained. Also, the existence of optimal control is proved, and the first-order and second-order optimality conditions satisfied by optimal control are verified. In particular, the optimal control is demonstrated to be of Bang-Bang form. |
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| Keywords: | Pest control global existence and uniqueness positive solutions optimal control Bang-Bang control |
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