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.

中文翻译：

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一类带参数的椭圆半变分不等式及其渐近行为的分布式最优控制问题

在本文中，我们研究了由一类带参数的椭圆边界半变分不等式支配的系统的内能最优控制问题。该系统起源于稳态热传导问题，该问题在局部 Lipschitz 函数的 Clarke 广义梯度描述的域边界的一部分上具有非单调多值次微分边界条件。我们证明了最优控制的存在性结果，并且当参数（如传热系数）在边界的一部分上趋于无穷大时，我们展示了最优控制和系统状态的渐近结果。