- About this Journal ·
- Abstracting and Indexing ·
- Advance Access ·
- Aims and Scope ·
- Annual Issues ·
- Article Processing Charges ·
- Articles in Press ·
- Author Guidelines ·
- Bibliographic Information ·
- Citations to this Journal ·
- Contact Information ·
- Editorial Board ·
- Editorial Workflow ·
- Free eTOC Alerts ·
- Publication Ethics ·
- Reviewers Acknowledgment ·
- Submit a Manuscript ·
- Subscription Information ·
- Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 739462, 12 pages
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.
- V. I. Arnold, Lectures on Partial Differential Equations, Springer, Berlin, Germany, 2004.
- L. C. Evans, Partial Differential Equations, vol. 19 of Graduate Studies in Mathematics, American Mathematical Society, Providence, RI, USA, 1998.
- S. Kovalevskaia, “Zur Theorie der partiellen differentialgleichung,” Journal für die reine und angewandte Mathematik, vol. 80, pp. 1–32, 1875.
- E. E. Rosinger, “Global version of the Cauchy-Kovalevskaia theorem for nonlinear PDEs,” Acta Applicandae Mathematicae, vol. 21, no. 3, pp. 331–343, 1990.
- J.-F. Colombeau, New Generalized Functions and Multiplication of Distributions, vol. 84, North-Holland, Amsterdam, The Netherlands, 1984.
- M. B. Oberguggenberger and E. E. Rosinger, Solution of Continuous Nonlinear PDEs through Order Completion, vol. 181, North-Holland, Amsterdam, The Netherlands, 1994.
- R. Anguelov and E. E. Rosinger, “Solving large classes of nonlinear systems of PDEs,” Computers & Mathematics with Applications, vol. 53, no. 3-4, pp. 491–507, 2007.
- J. H. van der Walt, “The uniform order convergence structure on ,” Quaestiones Mathematicae, vol. 31, no. 1, pp. 55–77, 2008.
- J. H. van der Walt, “The order completion method for systems of nonlinear PDEs: pseudo-topological perspectives,” Acta Applicandae Mathematicae, vol. 103, no. 1, pp. 1–17, 2008.
- J. H. van der Walt, “The order completion method for systems of nonlinear PDEs revisited,” Acta Applicandae Mathematicae, vol. 106, no. 2, pp. 149–176, 2009.
- R. Baire, Lecons Sur Les Fonctions Discontinues, Collection Borel, Paris, France, 1905.
- R. Anguelov, “Dedekind order completion of by Hausdorff continuous functions,” Quaestiones Mathematicae, vol. 27, no. 2, pp. 153–169, 2004.
- R. P. Dilworth, “The normal completion of the lattice of continuous functions,” Transactions of the American Mathematical Society, vol. 68, pp. 427–438, 1950.
- J. H. van der Walt, “The completion of uniform convergence spaces and an application to nonlinear PDEs,” Quaestiones Mathematicae, vol. 32, no. 3, pp. 371–395, 2009.
- R. Beattie and H.-P. Butzmann, Convergence Structures and Applications to Functional Analysis, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2002.
- O. Forster, Analysis 3, Integralrechnung im ℝn mit Anwendungen, vol. 52, Vieweg, Braunschweig, Germany, 1981.
- L. Hörmander, Linear Partial Differential Operators, Springer, Berlin, Germany, 1976.