Hyperbolic partial differential equations in a complete linear normed vector space
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Authors
Goulet, John A.
Issue Date
1976-08
Type
Electronic thesis
Thesis
Thesis
Language
ENG
Keywords
Mathematics
Alternative Title
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
School of
Full Citation
Publisher
Rensselaer Polytechnic Institute, Troy, NY