Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique
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...
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| Format: | Article |
| Language: | English |
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AIMS Press
2024-09-01
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| Series: | Mathematical Modelling and Control |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2024027 |
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| author | Bader Saad Alshammari Daoud Suleiman Mashat Fouad Othman Mallawi |
| author_facet | Bader Saad Alshammari Daoud Suleiman Mashat Fouad Othman Mallawi |
| author_sort | Bader Saad Alshammari |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-6b5414ab4c284686b139297c7bd407c5 |
| institution | Kabale University |
| issn | 2767-8946 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj-art-6b5414ab4c284686b139297c7bd407c52025-01-24T01:02:08ZengAIMS PressMathematical Modelling and Control2767-89462024-09-014333634910.3934/mmc.2024027Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization techniqueBader Saad Alshammari0Daoud Suleiman Mashat1Fouad Othman Mallawi2Department of Mathematics, College of Science, Northern Border University, Arar, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaThe 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.https://www.aimspress.com/article/doi/10.3934/mmc.2024027reaction-advection-diffusion equationpenalization techniqueboundary optimal controlconvergence |
| spellingShingle | Bader Saad Alshammari Daoud Suleiman Mashat Fouad Othman Mallawi Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique Mathematical Modelling and Control reaction-advection-diffusion equation penalization technique boundary optimal control convergence |
| title | Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique |
| title_full | Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique |
| title_fullStr | Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique |
| title_full_unstemmed | Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique |
| title_short | Numerical investigation for a boundary optimal control of reaction-advection-diffusion equation using penalization technique |
| title_sort | numerical investigation for a boundary optimal control of reaction advection diffusion equation using penalization technique |
| topic | reaction-advection-diffusion equation penalization technique boundary optimal control convergence |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2024027 |
| work_keys_str_mv | AT badersaadalshammari numericalinvestigationforaboundaryoptimalcontrolofreactionadvectiondiffusionequationusingpenalizationtechnique AT daoudsuleimanmashat numericalinvestigationforaboundaryoptimalcontrolofreactionadvectiondiffusionequationusingpenalizationtechnique AT fouadothmanmallawi numericalinvestigationforaboundaryoptimalcontrolofreactionadvectiondiffusionequationusingpenalizationtechnique |