The order completion method for systems of nonlinear PDEs: Pseudo-topological perspectives

2007/06/27 by Jan Harm van der Walt, van der Walt, Jan Harm
Computer Science · Mathematics · #06B30 #34A34 #46E05 #54A20 #Advanced Optimization Algorithms Research #FOS: Mathematics #Fractional Differential Equations Solutions #General Mathematics (math.GM) #Optimization and Variational Analysis #math.GM #msc:06B30 #msc:34A34 #msc:46E05 #msc:54A20

paper · pdf · doi:10.48550/arxiv.0706.3990

18 pages

arxiv created 2007/06/27 · openalex publication_date 2007/06/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Hausdorff continuous solutions of nonlinear PDEs through the order completion method

Related

• The order completion method for systems of nonlinear PDEs revisited
• Can there be a general nonlinear PDE theory for the existence of solutions ?
• Solving General Equations by Order Completion
• Solving large classes of nonlinear systems of PDEs
• Hausdorff continuous solutions of arbitrary continuous nonlinear PDEs through the order completion method