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Optimality for Control Problem with PDEs of Second-Order as Constraints

Author

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  • Savin Treanţă

    (Department of Applied Mathematics, University Politehnica of Bucharest, 060042 Bucharest, Romania)

  • Muhammad Bilal Khan

    (Department of Mathematics, COMSATS University Islamabad, Islamabad 44000, Pakistan)

  • Tareq Saeed

    (Nonlinear Analysis and Applied Mathematics—Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, Jeddah 21589, Saudi Arabia)

Abstract

This paper deals with a class of second-order partial differential equation (in short, PDE) constrained optimal control problems. More specifically, by using appropriate variational techniques, we state necessary conditions of optimality associated with this class of optimization problems, defined by controlled curvilinear integral cost functionals involving partial derivatives of second-order. The importance of the considered problem is provided by its applications in mechanics and physics. Compared with other research works, here we develop a new mathematics context that extends the results obtained so far, both through the use of controlled curvilinear integrals and also by considering partial derivatives of second-order. In addition, to emphasize the usefulness of the main results, an illustrative example is provided.

Suggested Citation

  • Savin Treanţă & Muhammad Bilal Khan & Tareq Saeed, 2022. "Optimality for Control Problem with PDEs of Second-Order as Constraints," Mathematics, MDPI, vol. 10(6), pages 1-7, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:977-:d:774277
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    References listed on IDEAS

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    1. Savin Treanţă, 2021. "Second-Order PDE Constrained Controlled Optimization Problems with Application in Mechanics," Mathematics, MDPI, vol. 9(13), pages 1-7, June.
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    Cited by:

    1. Savin Treanţă, 2022. "Recent Advances of Constrained Variational Problems Involving Second-Order Partial Derivatives: A Review," Mathematics, MDPI, vol. 10(15), pages 1-13, July.

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