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Volume 6, Issue 5, 1 October 2022, Pages 535-549
Abstract. 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 was 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.
How to Cite this Article:
Carolina M. Bollo, Claudia M. Gariboldi, Domingo A. Tarzia, Simultaneous distributed and Neumann boundary optimal control problems for elliptic hemivariational inequalities, J. Nonlinear Var. Anal. 6 (2022), 535-549.