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Analysis of coupled PDE systems modelling micro-electro-mechanical systems

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HeR_0921_macsSS.pdf (2.625Mb)
Date
2021-09
Author
He, Runan
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Abstract
This thesis studies some mathematical models for a Micro-Electro-Mechanical System (MEMS) capacitor, consisting of a fixed plate and a flexible plate separated by a fluid. It investigates the wellposedness of solutions to the resulting quasilinear coupled systems, as well as the finite-time blow-up (quenching) of solutions. The models considered include a parabolic-dispersive system modelling the fluid flow under an elastic plate, a parabolic-hyperbolic system for a thin membrane, as well as an elliptic-dispersive system for quasistatic fluid flow under an elastic plate. Short-time existence, uniqueness and smoothness are obtained by combining wellposedness results for a single equation with an abstract semigroup approach for the system. Quenching is shown to occur, if the solution ceases to exist after a finite time. The thesis concludes with a study of self-similar quenching solutions and their stability for a simple hyperbolic membrane model for a MEMS capacitor.
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http://hdl.handle.net/10399/4629
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©Heriot-Watt University, Edinburgh, Scotland, UK EH14 4AS.

Maintained by the Library
Tel: +44 (0)131 451 3577
Library Email: libhelp@hw.ac.uk
ROS Email: open.access@hw.ac.uk

Scottish registered charity number: SC000278

  • About
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  • Policies
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AboutCopyright
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