Distributed optimal control problems for a class of elliptic hemivariational inequalities with a parameter and its asymptotic behavior

GARIBOLDI, CLAUDIA M.; TARZIA, DOMINGO A.

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION

ELSEVIER SCIENCE BV

Año: 2022 vol. 104 p. 1 - 9

1007-5704

In this paper, we study optimal control problems on the internal energy 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 optimal controls and we show an asymptotic result for the optimal controls and the system states, when the parameter, like a heat transfer coefficient, tends to infinity on a portion of the boundary.