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The optimal control of an evolutionary boundary value problem | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 22، دوره 14، شماره 1، فروردین 2023، صفحه 263-274 اصل مقاله (431.6 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2022.24883.2843 | ||
| نویسندگان | ||
| Aissa Benseghir؛ Hamid Benseridi* ؛ Mourad Dilmi | ||
| Applied Mathematical Laboratory (LaMa), Faculty of Sciences, University of Setif 1- SETIF, 19000, Algeria | ||
| تاریخ دریافت: 22 مهر 1400، تاریخ بازنگری: 29 دی 1400، تاریخ پذیرش: 29 اسفند 1400 | ||
| چکیده | ||
| We consider a nonlinear initial boundary value problem in a two-dimensional rectangle. We derive variational formulation of the problem which is in the form of an evolutionary variational inequality in a product Hilbert space. Then, we establish the existence of a unique weak solution to the problem and prove the continuous dependence of the solution with respect to some parematers. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result. | ||
| کلیدواژهها | ||
| nonlinear boundary value problem؛ evolutionary inequality؛ weak solution؛ convergence results؛ optimal control | ||
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