Abstract
In this chapter, we study a size-structured population model with time-dependent diffusion rate. Due to seasonal variation in the rate at which individuals move from one region to another, it is natural to consider time-varying diffusion rate. We derive important estimates on mild solution. We also study the optimal control problem with pest population in mind. Necessary optimality conditions of first order are derived with the help of adjoint system. We prove the existence and uniqueness of optimal birth control by means of Ekeland’s variational principle.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
R. Liu, G. Liu, Optimal birth control problems for a nonlinear vermin population model with size-structure. J. Math. Anal. Appl. 449(1), 265–291 (2017)
Z.R. He, Y. Liu, An optimal birth control problem for a dynamical population model with size-structure. Nonlinear Anal. Real World Appl. 13(3), 1369–1378 (2012)
V. Barbu, M. Iannelli, Optimal control of population dynamics. J. Optim. Theory Appl. 102(1), 1–14 (1999)
S. Anita, Analysis and Control of Age-Dependent Population Dynamics, Mathematical Modelling: Theory and Applications, vol. 11 (Kluwer, Dordrecht, 2000)
N. Kato, Abstract linear partial differential equations related to size-structured population models with diffusion. J. Math. Anal. Appl. 436(2), 890–910 (2016)
A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations. Applied Mathematical Sciences (Springer, New York, 1983)
M. Kumar, S. Abbas, Optimal birth control for a size-structured population model with diffusion (2021). Preprint, arXiv:2103.08399
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Kumar, M., Abbas, S. (2022). Optimal Birth Control of Population Dynamics with Time-Varying Diffusivity Coefficient. In: Lacarbonara, W., Balachandran, B., Leamy, M.J., Ma, J., Tenreiro Machado, J.A., Stepan, G. (eds) Advances in Nonlinear Dynamics. NODYCON Conference Proceedings Series. Springer, Cham. https://doi.org/10.1007/978-3-030-81170-9_15
Download citation
DOI: https://doi.org/10.1007/978-3-030-81170-9_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-81169-3
Online ISBN: 978-3-030-81170-9
eBook Packages: EngineeringEngineering (R0)