Open AccessNew discussion concerning to optimal control for semilinear population dynamics system in Hilbert spaces
Author(s) -
Rohit Patel,
Anurag Shukla,
Juan J. Nieto,
V. Vijayakumar,
Shimpi Singh Jadon
Publication year - 2022
Publication title -
nonlinear analysis
Language(s) - English
Resource type - Journals
eISSN - 2335-8963
pISSN - 1392-5113
DOI - 10.15388/namc.2022.27.26407
Subject(s) - semigroup , mathematics , hilbert space , optimal control , population , nonlinear system , simple (philosophy) , state (computer science) , fixed point , pure mathematics , mathematical analysis , mathematical optimization , algorithm , philosophy , physics , demography , epistemology , quantum mechanics , sociology
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.