The order completion method for systems of nonlinear PDEs revisited

2008/03/03 by Jan Harm van der Walt, J. H. van der Walt, van der Walt, J. H.
Mathematics · #06B30 #34A34 #46E05 #54A20 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fractional Differential Equations Solutions #General Topology (math.GN) #Mathematical and Theoretical Analysis #math.AP #math.GN #msc:06B30 #msc:34A34 #msc:46E05 #msc:54A20

paper · pdf · doi:10.48550/arxiv.0803.0219

openalex publication_date 2008/03/03 · arxiv created 2008/04/23 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we presents further developments regarding the enrichment of the basic Theory of Order Completion. In particular, spaces of generalized functions are constructed that contain generalized solutions to all systems of continuous, nonlinear PDEs. In terms of the existence and uniqueness results previously obtained for such systems of equations, one may interpret the existence of generalized solutions presented here as a regularity result.

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