Hyperbolic partial differential equations in a complete linear normed vector space

Authors
Goulet, John A.
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Other Contributors
Diaz, Joaquin B., 1920-
Calinger, Ronald
Habetler, George J.
McLaughlin, H. W.
Issue Date
1976-08
Keywords
Mathematics
Degree
PhD
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This electronic version is a licensed copy owned by Rensselaer Polytechnic Institute, Troy, NY. Copyright of original work retained by author.
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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
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Rensselaer Theses and Dissertations Online Collection
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