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

• Autores: Jam Harm van der Walt
• Localización: Acta applicandae mathematicae, ISSN 0167-8019, Vol. 103, Nº. 1, 2008, págs. 1-17
• Idioma: inglés
• DOI: 10.1007/s10440-008-9214-6
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• Resumen

  • 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.