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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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/739462 |
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| _version_ | 1850218736714252288 |
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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 |
| id | doaj-art-7a32d5917dc7461fbeb03166d7225a69 |
| 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 |