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

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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.