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.

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