New discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces
Articles
Rohit Patel
Government P.G. College Bisalpur
https://orcid.org/0000-0002-0386-9401
Anurag Shukla
Rajkiya Engineering College Kannauj
https://orcid.org/0000-0001-5892-0342
Juan J. Nieto
Institute of Mathematics, University of Santiago de Compostela
https://orcid.org/0000-0001-8202-6578
Velusamy Vijayakumar
Vellore Institute of Technology
https://orcid.org/0000-0001-5976-5794
Shimpi Singh Jadon
Rajkiya Engineering College Kannauj
https://orcid.org/0000-0003-4953-7717
Published 2022-02-25
https://doi.org/10.15388/namc.2022.27.26407
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Keywords

population dynamics
diffusion
optimal control
Gronwall’s inequality

How to Cite

Patel, R. (2022) “New discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces”, Nonlinear Analysis: Modelling and Control, 27(3), pp. 496–512. doi:10.15388/namc.2022.27.26407.

Abstract

The objective of our paper is to investigate the optimal control of semilinear population dynamics system with diffusion using semigroup theory. The semilinear population dynamical model with the nonlocal birth process is transformed into a standard abstract semilinear control system by identifying the state, control, and the corresponding function spaces. The state and control spaces are assumed to be Hilbert spaces. The semigroup theory is developed from the properties of the population operators and Laplacian operators. Then the optimal control results of the system are obtained using the C0-semigroup approach, fixed point theorem, and some other simple conditions on the nonlinear term as well as on operators involved in the model.

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