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.
Highlights
Let us consider ζ, a bounded domain in Rn (n ∈ {1, 2, 3}) along the smooth boundary region ∂ζ
The life expectancy of individual is denoted by g+, σ(t, g, r) is known as the natural mortality rate, and α(t, g, r) is known as the natural fertility rate corresponding to individual of age g at location r ∈ ζ for the time t 0
The primary focus of our article is to prove the optimal control of the semilinear population dynamics system using C0-semigroup theory
Summary
Let us consider ζ, a bounded domain in Rn (n ∈ {1, 2, 3}) along the smooth boundary region ∂ζ. We have considered the following semilinear population dynamics model with nonlocal birth process:. In [22], the authors discussed the existing result for the mild solution and optimal control for fractional-order α ∈ In [1, 11, 19], the authors discussed the optimal control for the population of dynamics by different techniques. Taking the consideration of ideas from the above literature review and motivated by the fact, the optimal control of semilinear population dynamics system (1) is studied in the semigroup framework approach.
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