Controllability of a Fluid-Structure Interaction Arising in Chemical Vapor Deposition

化学气相沉积中流固耦合的可控性 在这个项目中，我们阐明了一个无限维控制问题所产生的使用化学气相沉积（CVD）在制造这种薄膜的表面上的基板;这种CVD是用于一系列的技术应用，包括微电路，化合物半导体器件和高性能的切割和研磨工具的建设。 在数学上，人们有一个版本的Navier-Stokes方程耦合到一个半线性热方程，控制（温度）的边界上的墙上实现。 为了确定通过控制壁温来提高膜生长质量的物理可行性，我们的目标是研究耦合偏微分方程的相关系统的可控性，在某种意义上的可控性将在下面进行精确描述。 在解决我们的控制理论问题时所采取的方法将是在分析“智能材料”技术时所看到的其他耦合偏微分方程所采用的方法。 在这项工作中，连续理论和近似理论都将被考虑。

Controllability of a Fluid-Structure Interaction Arising in Chemical Vapor Deposition In this project, we spell out an infinite dimensional control problem arising from the use of chemical vapor deposition (CVD) in the manufacture of this films on the surface of a substrate; this CVD is used in a host of technological applications, including the construction of microelectric circuitry, compound semiconductor devices and high-performance cutting and grinding tools. Mathematically, one has a version of the Navier-Stokes equations coupled to a semilinear heat equation, with the control (temperature) implemented on a wall of the boundary. With a view towards determining the physical feasibility of improving the quality of the film growth by controlling the wall temperature, we aim to study the controllability of the associated system of coupled partial differential equations, controllability in a sense to be made precise below. The approach to be taken in addressing our control theoretic question will be that adopted for other coupled partial differential equations seen in the analysis of "smart material" technology. Both continuous and approximation theory will be considered in this work.