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Global Well-Posedness and Exponential Stability for a Nonlinear Thermoelastic Kirchhoff-Love Plate System

Wan, Xiang
Format
Thesis/Dissertation; Online
Author
Wan, Xiang
Advisor
Lasiecka, Irena
Abstract
We study an initial-boundary-value problem for a quasilinear thermoelastic plate of Kirchhoff & Love-type with parabolic heat conduction due to Fourier, mechanically simply supported and held at the reference temperature on the boundary. For this problem, we show the short-time existence and uniqueness of classical solutions under appropriate regularity and compatibility assumptions on the data. Further, we use barrier techniques to prove the global existence and exponential stability of solutions under a smallness condition on the initial data. It is the first result of this kind established for a quasilinear non-parabolic thermoelastic Kirchhoff & Love plate in multiple dimensions.
Language
English
Published
University of Virginia, Department of Mathematics, PHD (Doctor of Philosophy), 2017
Published Date
2017-07-30
Degree
PHD (Doctor of Philosophy)
Collection
Libra ETD Repository
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