Affiliations: [a] Dipartimento di Matematica e Applicazioni “R. Caccioppoli”, Università degli Studi di Napoli “Federico II”, Complesso Monte S. Angelo, via Cintia, 80126 Napoli, Italy. E-mail: [email protected] | [b] Department of Differential Equations, Oles Honchar Dnipro National University, Gagarin av., 72, 49010 Dnipro, Ukraine. E-mail: [email protected] | [c] Department of Information Engineering, Electrical Engineering and Applied Mathematics, University of Salerno, Via Giovanni Paolo II, 132, Fisciano (SA), Italy. E-mail: [email protected]
Abstract: We study an optimal control problem for the mixed Dirichlet–Neumann boundary value problem for the strongly non-linear elliptic equation with exponential nonlinearity in a domain with rugous boundary. A density of surface traction u acting on a part of rugous boundary is taken as a control. The optimal control problem is to minimize the discrepancy between a given distribution and the current system state. We deal with such case of nonlinearity when we cannot expect to have a solution of the state equation for a given control. After having defined a suitable class of the weak solutions, we provide asymptotic analysis of the above mentioned optimal control problem posed in a family of perturbed domains and give the characterization of the limiting behavior of its optimal solutions.
