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Optimal Birth Control of Population Dynamics with Time-Varying Diffusivity Coefficient

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Advances in Nonlinear Dynamics

Part of the book series: NODYCON Conference Proceedings Series ((NCPS))

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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.

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Authors and Affiliations

  1. School of Basic Sciences, Indian Institute of Technology Mandi, Mandi, Himachal Pradesh, India

    Manoj Kumar & Syed Abbas

Authors
  1. Manoj Kumar
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  2. Syed Abbas
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Corresponding author

Correspondence to Syed Abbas .

Editor information

Editors and Affiliations

  1. Department of Structural and Geotechnical Engineering, Sapienza University of Rome, Rome, Italy

    Walter Lacarbonara

  2. Department of Mechanical Engineering, University of Maryland, College Park, MD, USA

    Balakumar Balachandran

  3. Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA, USA

    Michael J. Leamy

  4. Department of Physics, Lanzhou University of Technology, Lanzhou, Gansu, China

    Jun Ma

  5. ISEP-Institute of Engineering, Polytechnic of Porto, Porto, Portugal

    J. A. Tenreiro Machado

  6. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, Hungary

    Gabor Stepan

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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

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  • DOI: https://doi.org/10.1007/978-3-030-81170-9_15

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-81169-3

  • Online ISBN: 978-3-030-81170-9

  • eBook Packages: EngineeringEngineering (R0)

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