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.
Benseghir,A , Benseridi,H and Dilmi,M . (2023). The optimal control of an evolutionary boundary value problem. International Journal of Nonlinear Analysis and Applications, 14(1), 263-274. doi: 10.22075/ijnaa.2022.24883.2843
MLA
Benseghir,A , , Benseridi,H , and Dilmi,M . "The optimal control of an evolutionary boundary value problem", International Journal of Nonlinear Analysis and Applications, 14, 1, 2023, 263-274. doi: 10.22075/ijnaa.2022.24883.2843
HARVARD
Benseghir A, Benseridi H, Dilmi M. (2023). 'The optimal control of an evolutionary boundary value problem', International Journal of Nonlinear Analysis and Applications, 14(1), pp. 263-274. doi: 10.22075/ijnaa.2022.24883.2843
CHICAGO
A Benseghir, H Benseridi and M Dilmi, "The optimal control of an evolutionary boundary value problem," International Journal of Nonlinear Analysis and Applications, 14 1 (2023): 263-274, doi: 10.22075/ijnaa.2022.24883.2843
VANCOUVER
Benseghir A, Benseridi H, Dilmi M. The optimal control of an evolutionary boundary value problem. IJNAA. 2023;14(1):263-274. doi: 10.22075/ijnaa.2022.24883.2843
International Journal of Nonlinear Analysis and Applications