KUKU

KU ScholarWorks

  • myKU
  • Email
  • Enroll & Pay
  • KU Directory
    • Login
    View Item 
    •   KU ScholarWorks
    • Dissertations and Theses
    • Dissertations
    • View Item
    •   KU ScholarWorks
    • Dissertations and Theses
    • Dissertations
    • View Item
    JavaScript is disabled for your browser. Some features of this site may not work without it.

    Solutions of Lattice Differential Equations over Inhomogeneous Media

    Thumbnail
    View/Open
    BrucalHallare_ku_0099D_12423_DATA_1.pdf (885.7Kb)
    Issue Date
    2012-12-31
    Author
    Brucal-Hallare, Maila
    Publisher
    University of Kansas
    Format
    141 pages
    Type
    Dissertation
    Degree Level
    Ph.D.
    Discipline
    Mathematics
    Rights
    Copyright held by the author.
    Metadata
    Show full item record
    Abstract
    This thesis investigates one-dimensional spatially-discrete reaction-diffusion equations with a diffusion term that involves nearest-neighbor coupling and with a reaction-term that is a smooth-cubic nonlinearity. Specifically, we consider two nontrivial examples of lattice differential equations (LDEs) on Z that are related to the (homogeneous) lattice Nagumo equation. The LDEs that we consider are used to model natural phenomena defined over an inhomogeneous medium, namely: (1) a lattice Nagumo equation with a negative diffusion coefficient. Such is still a well-posed problem in the LDE setting and has been shown to arise from a discrete model of phase transition for shape memory alloys. This thesis shows that the anti-diffusion lattice Nagumo equation has a period-2 traveling wavefront solution that is stable and unique. Utilizing the concrete expressions for the nonlinearities, we obtain criteria on the (d, a)-parameter plane that guarantee a display of bistable and monostable dynamics. Where there's bistable dynamics, we study the propagation failure phenomenon; where there's monostable dynamics, we compute a minimum wave speed for the traveling waves. (2) a lattice Nagumo equation that has a single diffusion-defect in the middle of Z, which may occur due to deviations in the diffusive property of the medium. This thesis shows that such an equation has a time-global solution which behaves as two fronts coming from the both sides of Z. A key idea for the existence proof is a characterization of the asymptotic behavior of the solutions for negative time in terms of an appropriate super-solution, sub-solution pair.
    URI
    http://hdl.handle.net/1808/18632
    Collections
    • Dissertations [4660]
    • Mathematics Dissertations and Theses [179]

    Items in KU ScholarWorks are protected by copyright, with all rights reserved, unless otherwise indicated.


    We want to hear from you! Please share your stories about how Open Access to this item benefits YOU.


    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
     

     

    Browse

    All of KU ScholarWorksCommunities & CollectionsThis Collection

    My Account

    Login

    Statistics

    View Usage Statistics

    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
     

     

    The University of Kansas
      Contact KU ScholarWorks
    Lawrence, KS | Maps
     
    • Academics
    • Admission
    • Alumni
    • Athletics
    • Campuses
    • Giving
    • Jobs

    The University of Kansas prohibits discrimination on the basis of race, color, ethnicity, religion, sex, national origin, age, ancestry, disability, status as a veteran, sexual orientation, marital status, parental status, gender identity, gender expression and genetic information in the University’s programs and activities. The following person has been designated to handle inquiries regarding the non-discrimination policies: Director of the Office of Institutional Opportunity and Access, IOA@ku.edu, 1246 W. Campus Road, Room 153A, Lawrence, KS, 66045, (785)864-6414, 711 TTY.

     Contact KU
    Lawrence, KS | Maps