Date of Award
May 2021
Document Type
Dissertation
Degree Name
Doctor of Philosophy (PhD)
Department
Mathematical Sciences
Committee Member
Shitao Liu
Committee Member
Mishko Mitkovski
Committee Member
Jeong-Rock Yoon
Committee Member
Leo Rebholz
Abstract
In this dissertation we primarily focus on the Mindlin-Timoshenko (MT) plate system, which is a strongly coupled two dimensional system consisting of a wave equation and a system of isotropic elasticity, that arises in modeling plate vibrations especially at high frequencies and thicker plates. We prove two results regarding the MT system. Namely, the exact controllability of the system and an inverse problem result. We demonstrate the exact controllability of the system via an indirect control technique that proves a two-level indirect inverse observability estimate for the diagonalized system. For the inverse problem, we prove the global uniqueness of recovering the plate density from a single boundary measurement under appropriate geometrical assumptions. Both results incorporate the use of several different Carleman-type estimates derived for hyperbolic equations that we apply to a diagonalized version of the MT system. These diagonalizations consist of coupled systems of wave equations where coupling is maintained only in the lower order.
Recommended Citation
Kurz, Jason Alexander, "Exact Controllability and Inverse Problem for the Mindlin-Timoshenko System" (2021). All Dissertations. 2821.
https://tigerprints.clemson.edu/all_dissertations/2821