Date of Award
12-2016
Document Type
Thesis
Degree Name
Master of Science (MS)
Legacy Department
Mathematical Science
Committee Member
Dr. Shitao Liu, Committee Chair
Committee Member
Dr. Mishko Mitkovski, Co-Chair
Committee Member
Dr. Jeong-Rock Yoon
Committee Member
Dr. Taufiquar Khan
Abstract
In this thesis we investigate the boundary controllability of the wave and heat equa-tions with bounded potential in one dimension. This is done by way of the observability inequality. For the wave equation, we use the Hilbert Uniqueness Method of J. L. Lions to show the observability inequality is sufficient for exact controllability. Observability is shown by the multiplier method when there is no potential and a special Exchange of Vari-ables technique for when potential is present. Due to limitiations of this method we also use a Carleman Estimate which can be extended to higher dimensions. For the heat equation, we use a Variational Method to show observability is sufficient for null controllability. The proof of observability is accomplished by an analogous Carleman Estimate to that for the wave equation.
Recommended Citation
Green, Andrew Walton, "Boundary Controllability for One-Dimensional Wave and Heat Equations with Potential" (2016). All Theses. 2559.
https://tigerprints.clemson.edu/all_theses/2559