Generalized functions as a tool for nonsmooth nonlinear problems in mathematics and physics

2006/12/25 by J. F. Colombeau, Colombeau, J. F. · 1 citation
Computer Science · Mathematics · #35D05 #35D10 #35L67 #35Q72 #35R05 #46F30 #65M99 #73J30 #82D20 #83C57 #FOS: Mathematics #FOS: Physical sciences #General Mathematics (math.GM) #Mathematical Analysis and Transform Methods #Mathematical Physics (math-ph) #Mathematical and Theoretical Analysis #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.math-ph/0612077

openalex publication_date 2006/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A differential algebra of nonlinear generalized functions is presented as a tool for a wide range of nonsmooth nonlinear problems. The power of the differential algebra is used to do mathematical calculations or proofs; then the final result is often a classical function or distribution which is not solution in the classical or distributional sense. The aim of this text is to invite the readers in applying this tool in their own research without significant prerequisites by presenting its use on a sample of elementary applications from mathematics and physics. This text is the written version of a talk at the 2007 annual meeting of the AMS, NewOrleans, january 2007.

Citations

• Generalized Functions and Infinitesimals
• Generalized Solutions to Hyperbolic Systems with Nonlinear Conditions and Strongly Singular Data

Cited by

• Models of the "Universe" and a Closure Principle

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