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The Order Completion Method for Systems of Nonlinear PDEs: Pseudo-topological Perspectives

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Abstract

By setting up appropriate uniform convergence structures, we are able to reformulate the Order Completion Method of Oberguggenberger and Rosinger in a setting that more closely resembles the usual topological constructions for solving PDEs. As an application, we obtain existence and uniqueness results for the solutions of arbitrary continuous, nonlinear PDEs.

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Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, South Africa

    Jan Harm van der Walt

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  1. Jan Harm van der Walt
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Correspondence to Jan Harm van der Walt.

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van der Walt, J.H. The Order Completion Method for Systems of Nonlinear PDEs: Pseudo-topological Perspectives. Acta Appl Math 103, 1–17 (2008). https://doi.org/10.1007/s10440-008-9214-6

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  • DOI: https://doi.org/10.1007/s10440-008-9214-6

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