Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique

Bader Saad Alshammari; Daoud Suleiman Mashat; Fouad Othman Mallawi; Bader Saad Alshammari; Daoud Suleiman Mashat; Fouad Othman Mallawi

doi:10.3934/mmc.2024027

Mathematical Modelling and Control

2024, Volume 4, Issue 3: 336-349. doi: 10.3934/mmc.2024027

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Research article

Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique

1.
Department of Mathematics, College of Science, Northern Border University, Arar, Saudi Arabia
2.
Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 21 June 2023 Revised: 29 October 2023 Accepted: 12 January 2024 Published: 10 September 2024

The objective of this paper is to describe the problem of boundary optimal control of the reaction-advection-diffusion equation for not very regular Dirichlet data and enumerate its qualitative properties. We check that the state equation is well-posed and we introduce the penalization technique to take into account the boundary condition of the Dirichlet type. Then, we consider the corresponding optimal boundary control problem and give the optimality conditions. Finally, we conducted a numerical investigation of the convergence of the solution of the penalized problem to the solution of the non-penalized one when the penalty parameter tends to zero in regular and non-regular domains.
- reaction-advection-diffusion equation,
- penalization technique,
- boundary optimal control,
- convergence
Citation: Bader Saad Alshammari, Daoud Suleiman Mashat, Fouad Othman Mallawi. Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique[J]. Mathematical Modelling and Control, 2024, 4(3): 336-349. doi: 10.3934/mmc.2024027

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Abstract

The objective of this paper is to describe the problem of boundary optimal control of the reaction-advection-diffusion equation for not very regular Dirichlet data and enumerate its qualitative properties. We check that the state equation is well-posed and we introduce the penalization technique to take into account the boundary condition of the Dirichlet type. Then, we consider the corresponding optimal boundary control problem and give the optimality conditions. Finally, we conducted a numerical investigation of the convergence of the solution of the penalized problem to the solution of the non-penalized one when the penalty parameter tends to zero in regular and non-regular domains.

References

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