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arXiv · 2109.10668

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

Claudia M. Gariboldi·Domingo A. Tarzia
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Abstract

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.

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Claudia M. Gariboldi, Domingo A. Tarzia. 2021-09-22. Distributed optimal control problems for a class of elliptic hemivariational inequalities with a parameter and its asymptotic behavior. https://doi.org/10.1016/j.cnsns.2021.106027

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