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    Hyperbolic partial differential equations in a complete linear normed vector space

    Author
    Goulet, John A.
    View/Open
    177940_thesis.pdf (3.122Mb)
    Other Contributors
    Diaz, Joaquin B., 1920-; Calinger, Ronald; Habetler, George J.; McLaughlin, H. W.;
    Date Issued
    1976-08
    Subject
    Mathematics
    Degree
    PhD;
    Terms of Use
    This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.;
    Metadata
    Show full item record
    URI
    https://hdl.handle.net/20.500.13015/1868
    Abstract
    Existence and uniqueness results for the abstract partial differential equation of the form uxy=F( x,y,u,ux,uy), where values of the unknown function lies in an arbitrary Banach space. The solution is approximated by abstract"hyperbolic paraboloids", in a manner analogous to the classical method used in the existence proof for the ordinary differential equation dy/dx=F(x,y) using Cauchy-Euler polygons. Convergence is proven using the abstract versions of the theorems of Ascoli and Arzela; the latter in the case where derivatives of the solution are involved. Also used is a little known theorem of Mazur in proving pointwise compactness (as required by the Ascoli and Arzela theorems) of the aforementioned approximating sequences.;
    Description
    August 1976; School of
    Department
    Dept. of;
    Publisher
    Rensselaer Polytechnic Institute, Troy, NY
    Relationships
    Rensselaer Theses and Dissertations Online Collection;
    Access
    Restricted to current Rensselaer faculty, staff and students. Access inquiries may be directed to the Rensselaer Libraries.;
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    • RPI Theses Online (Complete)

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