We consider an optimal control problem for non-isothermal steady flows of low-concentrated aqueous polymer solutions in a bounded 3D domain. In this problem, the state functions are the flow velocity and the temperature, while the control function is the heat flux through a given part of the boundary of the flow domain. We obtain sufficient conditions for the existence of weak solutions that minimize a cost functional under a given bounded set of admissible controls. It is shown that the marginal function of the considered control system is lower semi-continuous and the optimal states operator generates a continuous branch in a suitable function space.

中文翻译：

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聚合物流体的Boussinesq逼近的最佳边界控制

我们考虑有界3D域中低浓度聚合物水溶液的非等温稳定流动的最优控制问题。在这个问题中，状态函数是流速和温度，而控制函数是通过流域边界的给定部分的热通量。我们为弱解的存在获得了充分的条件，这些弱解在给定的可控制范围内将成本函数最小化。结果表明，所考虑的控制系统的边际函数是较低的半连续的，最优状态算子在合适的函数空间中产生了一个连续的分支。