Colombeau solutions to nonlinear wave equations

2006/12/15 by Michael Oberguggenberger, Oberguggenberger, Michael · 1 citation
Mathematics · #35D05 #35L60 #46F30 #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical and Theoretical Analysis #math.AP #msc:35D05 #msc:35L60 #msc:46F30

paper · pdf · doi:10.48550/arxiv.math/0612445

14 pages

arxiv created 2006/12/15 · openalex publication_date 2006/12/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is a tutorial that demonstrates various methods from the Colombeau theory of generalized functions in the context of semilinear wave equations. The Colombeau generalized functions constitute differential algebras that contain the space of distributions. We solve the 1D-semilinear wave equation in these algebras, show how delta waves can be computed and then turn to linear and nonlinear regularity theory.

Cited by

• The sequence of ideas in a re-discovery of the Colombeau algebras

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