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    Controllability of non-self-adjoint systems of partial differential equations

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    Author
    Park, Jeff
    Chair
    Avdonin, Sergei
    Committee
    Rhodes, John
    Allman, Elizabeth
    Rybkin, Alexei
    Keyword
    Nonselfadjoint operators
    Differential equations
    Schrödinger equation
    Metadata
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    URI
    http://hdl.handle.net/11122/13126
    Abstract
    In this dissertation, we first consider the problem of exact controllability of a system of N one-dimensional coupled wave equations when the control is exerted on a part of the boundary by means of one control. We provide a Kalman condition (necessary and sufficient) and give a description of the attainable set. The second problem we consider is the inverse problem for the vector Schrödinger equation on the interval with a non-self-adjoint matrix potential. In doing so, we prove controllability of the system and develop a method to recover spectral data from the system. Then, we solve the inverse problem using techniques of the Boundary Control method. The final problem is that of internal null controllability of a beam equation on an interval. We provide a partial characterization for controllability for arbitrary open subsets where the control is applied.
    Description
    Dissertation (Ph.D.) University of Alaska Fairbanks, 2022
    Table of Contents
    Chapter 1: Introduction -- Chapter 2: Introduction to the Kalman Condition for the boundary controllability of coupled 1-d wave equations -- Chapter 3: The Kalman condition for the boundary controllability of coupled 1-d wave equations -- Chapter 4: Introduction to inverse problem for the Schrödinger Equation with non-self-adjoint matrix potential -- Chapter 5: Inverse problem for the Schrödinger Equation with non-self-adjoint matrix potential -- Chapter 6: Introduction to internal controllability of the beam equation with structural damping -- Chapter 7: Internal controllability of the beam equation with structural damping -- Chapter 8: Conclusion and future work -- References.
    Date
    2022-12
    Type
    Dissertation
    Collections
    Mathematics and Statistics

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