Author
Goulet, John A.
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.;
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.;