Control Problems for Strongly Coupled Non-Linear Partial Differential Equations

本研究项目的目的是研究相互作用结构的控制，优化，稳定性和长时间的行为，这是数学建模的非齐次系统的强耦合偏微分方程的界面。描述整个结构的每个组成部件以及它们之间的耦合的单个偏微分方程可以是线性的或非线性的、色散的和振荡的。brbr调查将首先在四个典型的互动结构激励类上进行。它们的目的是作为基准的情况下，物理上重要的互动和非平凡耦合偏微分方程的一般主题。它们是：（1）结构声室中的降噪问题，采用“智能材料/结构”技术;（2）二维机翼在亚音速或超音速三维气流中的气动弹性颤振控制;（3）磁流体动力学方程控制中的等离子体加热和等离子体约束;（4）粘性不可压缩流体动力学中湍流的渐近抑制。

The present research project aims at investigating the properties of control, optimization, stability and long-time behavior of interactive structures, which are mathematically modeled by inhomogeneous systems of strongly coupled partial differential equations with an interface. Both the single partial differential equations describing each a constitutive component of the overall structure as well as the coupling between them, may be linear or non-linear, dispersive, and oscillatory. brbr Investigation will be carried out initially on four canonical motivating classes of interactive structures. They are intended to serve as benchmark cases for the general topic of physically significant interactive and non-trivially coupled Partial Differential Equations. They are: (1) the noise reduction problem in a structural acoustic chamber, by use of 'smart material/structure' technology; (2) flutter control of a 2-dimensional wing immersed in a subsonic or supersonic 3-dimensional gas flow in aeroelasticity; (3) plasma heating and plasma confinement in the control of magnetohydrodynamics equations; (4) asymptotic suppression of turbulence in viscous incompressible fluid dynamics.