First-order necessary conditions of optimality for the optimal control of two-dimensional convective Brinkman–Forchheimer equations with state constraints

Abstract

This work is concerned about some distributed optimal control problems governed by two-dimensional convective Brinkman–Forchheimer (CBF) equations, which describe the motion of incompressible viscous fluid through a rigid, homogeneous, isotropic, porous medium. We address a distributed optimal control problem of minimizing a suitable cost functional subjected to 2D CBF equations with state constraints. We establish the existence of an optimal solution and obtain the first-order necessary conditions of optimality for such optimal control problems.

Keywords:

• Porus medium
• convective Brinkman–Forchheimer equations
• first-order necessary conditions
• state constraints
• optimal control

Mathematics Subject Classification (2010):

• 49J20
• 35Q35
• 76D03

Acknowledgements

M. T. Mohan would like to thank the Department of Science and Technology (DST), India for Innovation in Science Pursuit for Inspired Research (INSPIRE) Faculty Award (IFA17-MA110). The author sincerely would like to thank the reviewers for their valuable comments and suggestions, which helped us to improve the manuscript significantly.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.