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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 739462, 12 pages
http://dx.doi.org/10.1155/2013/739462
Research Article

The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems

Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria 0002, South Africa

Received 18 July 2012; Revised 11 September 2012; Accepted 16 September 2012

Academic Editor: Svatoslav Stanek

Copyright © 2013 Jan Harm van der Walt. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present an existence result for generalized solutions of initial value problems obtained through the order completion method. The solutions we obtain satisfy the initial condition in a suitable extended sense, and each such solution may be represented in a canonical way through its generalized partial derivatives as nearly finite normal lower semicontinuous function.