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    Long time behavior and stability of special solutions of nonlinear partial differential equations.

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    Demirkaya_ku_0099D_11377_DATA_1.pdf (664.6Kb)
    Issue Date
    2011-04-21
    Author
    Demirkaya, Aslihan
    Publisher
    University of Kansas
    Format
    118 pages
    Type
    Dissertation
    Degree Level
    Ph.D.
    Discipline
    Mathematics
    Rights
    This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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    Abstract
    In this dissertation, in the first part, I study the long-time behavior of the solutions of the Kuramoto-Sivashinsky equation and the Burgers-Sivashinsky equation. First, I work on a two-dimensional modified KS equation and prove the existence of a global attractor on a bounded domain. Next, I study the long-time behavior of the solutions of the one-dimensional BS equation for general initial data as opposed to the usually considered odd initial data. Third, I study the long-time behavior of radially symmetric solutions of the KS equation in a shell domain in three-dimensions. In the second part, we deal with the conditional stability of radial steady state solutions for the one-dimensional Klein-Gordon equation. I consider the one-dimensional case and construct the infinite-dimensional invariant manifolds explicitly. The result is a precise center-stable manifold theorem, which includes the co-dimension of the manifolds and the decay rates.
    URI
    http://hdl.handle.net/1808/7695
    Collections
    • Dissertations [4472]
    • Mathematics Dissertations and Theses [180]

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    785-864-8983
    KU Libraries
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    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
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    Contact KU ScholarWorks
    785-864-8983
    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    785-864-8983

    KU Libraries
    1425 Jayhawk Blvd
    Lawrence, KS 66045
    Image Credits
     

     

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