Date of Award
Master of Science (MS)
Dr. Shitao Liu, Committee Chair
Dr. Mishko Mitkovski, Co-Chair
Dr. Jeong-Rock Yoon
Dr. Tauﬁquar Khan
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.
Green, Andrew Walton, "Boundary Controllability for One-Dimensional Wave and Heat Equations with Potential" (2016). All Theses. 2559.