Solving a characteristic Cauchy problem

2008/11/14 by Emmanuel Allaud, Allaud, Emmanuel, Victor Devoue +1
Mathematics · #35D05 (Primary) #35L05 (Secondary) #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35D05 #msc:35L05

paper · pdf · doi:10.48550/arxiv.0811.2256

23 pages; no figure

arxiv created 2008/11/14 · arxiv updated 2009/12/01

Abstract

In this paper we give a meaning to the nonlinear characteristic Cauchy problem for the Wave Equation in base form by replacing it by a family of non-characteristic problems in an appropriate algebra of generalized functions. We prove existence of a solution and we precise how it depends on the choice made. We also check that in the classical case (non-characteristic) our new solution coincides with the classical one.

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