Simultaneous distributed and Neumann boundary optimal control problems for elliptic hemivariational inequalities

C.M. BOLLO; C. M. GARIBOLDI; D.A. TARZIA

Journal of Nonlinear and Variational Analysis

Biemdas Academic Publishers

Año: 2022 vol. 6 p. 535 - 549

2560-6921

In this paper, we study boundary optimal control problems on the heat flux and simultaneous distributed-boundary optimal control problems on the internal energy and the heat flux for a system governed by a class of elliptic boundary hemivariational inequalities with a parameter. The system has been originated by a steady-state heat conduction problem with non-monotone multivalued subdifferential boundary condition on a portion of the boundary of the domain described by the Clarke generalized gradient of a locally Lipschitz function. We prove an existence result for the boundary optimal control problem and simultaneous distributed-boundary optimal control problems. We show an asymptotic behavior result for the optimal controls and the system states for both optimal control problems, when the parameter, like a heat transfer coefficient, tends to infinity on a portion of the boundary.