论文标题
固定Navier-Stokes方程的半体体不平等：存在，依赖和最佳控制
Hemivariational inequality for stationary Navier-Stokes equations: existence, dependence and optimal control
论文作者
论文摘要
在本文中，我们研究了有关固定的Navier-Stokes方程的一类半传递不平等的解决方案的依赖性和最佳控制结果，但没有使用伪单酮操作员理论。为此，由于J. Rauch，我们考虑了一个经典的假设，这使我们限制了解决方案的定义。劳奇的假设，尽管确保了溶液的存在，但不允许结论非凸功能是局部lipchitz。此外，证明了两个依赖性结果，一个相对于边界条件的变化，另一个相对于外力的密度。后来的一个将用于证明存在于分布式参数最佳控制问题的最佳控制，其中控制由外部力表示。
In this paper we study existence, dependence and optimal control results concerning solutions to a class of hemivariational inequalities for stationary Navier-Stokes equations but without making use of the theory of pseudo-monotone operators. To do so, we consider a classical assumption, due to J. Rauch, which constrains us to make a slight change on the definition of a solution. The Rauch assumption,, although insure the existence of a solution, does not allow the conclusion that the non-convex functional is locally Lipschitz. Moreover, two dependence results are proved, one with respect to changes of the boundary condition and the other with respect to the density of external forces. The later one will be used to prove the existence of an optimal control to the distributed parameter optimal control problem where the control is represented by the external forces.
