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

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 pa...

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Main Author: Jan Harm van der Walt
Format: Article
Language:English
Published: Wiley 2013-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2013/739462
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author Jan Harm van der Walt
author_facet Jan Harm van der Walt
author_sort Jan Harm van der Walt
collection DOAJ
description 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.
format Article
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institution OA Journals
issn 1085-3375
1687-0409
language English
publishDate 2013-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-7a32d5917dc7461fbeb03166d7225a692025-08-20T02:07:37ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/739462739462The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value ProblemsJan Harm van der Walt0Department of Mathematics and Applied Mathematics, University of Pretoria, Lynwood Road, Pretoria 0002, South AfricaWe 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.http://dx.doi.org/10.1155/2013/739462
spellingShingle Jan Harm van der Walt
The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
Abstract and Applied Analysis
title The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
title_full The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
title_fullStr The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
title_full_unstemmed The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
title_short The Order Completion Method for Systems of Nonlinear PDEs: Solutions of Initial Value Problems
title_sort order completion method for systems of nonlinear pdes solutions of initial value problems
url http://dx.doi.org/10.1155/2013/739462
work_keys_str_mv AT janharmvanderwalt theordercompletionmethodforsystemsofnonlinearpdessolutionsofinitialvalueproblems
AT janharmvanderwalt ordercompletionmethodforsystemsofnonlinearpdessolutionsofinitialvalueproblems