The optimal control of an evolutionary boundary value problem
نویسندگان
1 Applied Mathematical Laboratory (LaMa), Faculty of Sciences, University of Setif 1- SETIF, 19000, Algeria
2 Applied Mathematical Laboratory (LaMa), Faculty of Sciences, University of Setif 1- SETIF, 19000, Algeria
3 Applied Mathematical Laboratory (LaMa), Faculty of Sciences, University of Setif 1- SETIF, 19000, Algeria
doi
10.22075/ijnaa.2022.24883.2843چکیده
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.
