Generalized solutions to nonlinear first order Cauchy problems

2007/09/13 by Jan Harm van der Walt, van der Walt, Jan Harm
Mathematics · #Mathematical and Theoretical Analysis #Nonlinear Differential Equations Analysis #math.AP #math.GN #msc:35B30 #msc:35F10 #msc:46A19

paper · pdf · doi:10.48550/arxiv.0709.1994

arxiv created 2007/09/13 · arxiv updated 2009/12/01

Abstract

The recent significant enrichment of the Order Completion Method for nonlinear Systems of PDEs resulted in the global existence of generalized solutions to a large class of such equations. In this paper we investigate the existence and regularity of the generalized solutions to a family of nonlinear first order Cauchy problems. The spaces of generalized solutions are obtained as the completions of suitably constructed uniform convergence spaces.

Related

• Solutions of nonlinear PDEs in the completion of uniform convergence spaces
• The order completion method for systems of nonlinear PDEs revisited
• Solving large classes of nonlinear systems of PDEs
• Solving General Equations by Order Completion
• The uniform order convergence structure on ML(X)