标题： 粘弹性半可压缩流体流动的最优控制 显示英文标题

标题： Optimal control of flows of viscoelastic semi-compressible fluids

摘要： 半线性抛物系统具有双线性非线性项，具有许多应用，其最优控制导致相对简单的最优条件。 一个例子是不可压缩的纳维-斯托克斯系统，用于均质流体，但此处修改为物理上合理的轻微（所谓“半”）可压缩液体模型，而不是完全可压缩气体。 考虑了一个优化边界压力的最优控制问题，并在简单变体中分析了控制到状态映射的唯一性和二维情况下的第一阶最优条件，并在非简单变体中概述了三维情况。 其他一些双线性抛物系统，如Cahn-Hilliard扩散或磁流体动力学，可以类似地处理。 显示英文摘要

摘要： Semilinear parabolic systems with bi-linear nonlinearities cover a lot of applications and their optimal control leads to relatively simple optimality conditions. An example is the incompressible Navier-Stokes system for homogeneous fluids, which is however here modified towards a physically reasonable model of slightly (so-called ``semi'') compressible liquids rather than fully compressible gases. An optimal control problem optimizing also pressure on the boundary is considered and, in the simple variant, analysed as far as uniqueness of the control-to-state mapping and 1st-order optimality conditions in the 2-dimensional case and outlined in a nonsimple variant for the 3-dimensional case. Some other bi-linear parabolic systems as Cahn-Hilliard diffusion or magneto-hydrodynamics can be treated analogously.