On a class of algebras of generalized functions. Application to differential systems
type: Item
instance of: scholarly article
title: On a class of algebras of generalized functions. Application to differential systems
zbMATH Open document ID: 0887.46015
published in: Annales Mathématiques Blaise Pascal
publication date: 1997-10-06T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/79178
review text: In order to study partial differential equations having no distributional solutions, various algebras of generalized functions have been introduced [see e.g. the monograph of \textit{J. F. Colombeau}, ``Elementary introduction to new generalized functions'' (1985; Zbl 0584.46024) and a paper of \textit{Y. V. Egorov}, Russ. Math. Surveys 45, No. 5, 1-49 (1990; Zbl 0754.46034)]. In the paper under review, the author introduces, in terms of nonstandard analysis, yet another type of these algebras, called asymptotic algebras. Applications to differential problems are given.
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 46S20
Mathematics Subject Classification ID: 46J15
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 03H05
zbMATH DE Number: 1053375
zbMATH Keywords: partial differential equations having no distributional solutions
zbMATH Keywords: nonstandard analysis
author: Antoine Delcroix
reviewed by: Raymond Mortini
MaRDI profile type: Publication
OpenAlex ID: W2315727264
cites work: Trivial solutions for a non-lineartwo-space dimensional wave equation perturbed by space-time white noise
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DOI: 10.5802/AMBP.85
description: scientific article; zbMATH DE number 1053375