PDE and extrafunctions
type: Item
instance of: scholarly article
title: PDE and extrafunctions
zbMATH Open document ID: 1068.35026
published in: Rocky Mountain Journal of Mathematics
publication date: 2005-03-11T00:00:00Z
review text: Based on the first author's construction of hyperreal numbers and hyperfunctionals [Lect. Notes Pure Appl. Math. 238, 81--117, Dekker, New York (2004; Zbl 1094.46508)]. The present paper investigates solvability of linear first order Cauchy problems in a similar setting of generalized functions, the space of extrafunctions. It is shown that solutions exist under mild assumptions, although uniqueness is not attainable. Finally, the relationship between extrafunctions and Schwartz-, Egorov-, and Colombeau generalized functions is explored. It should be noted, though, that several statements on Colombeau generalized functions included in the article are incorrect (e.g., it is claimed that the product of smooth functions is not preserved when embedding into the Colombeau algebra although in fact this is one of the distinguishing features of the construction). A similar criticism has to be made on the handling of the interrelationship between the various solution concepts.
reviewed by: Michael Kunzinger
Mathematics Subject Classification ID: 35D05
Mathematics Subject Classification ID: 46F99
Mathematics Subject Classification ID: 46F30
zbMATH DE Number: 2144257
zbMATH Keywords: hypernumbers
author: Mark Burgin
author: J. V. Ralston
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069831
OpenAlex ID: W2035914614
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DOI: 10.1216/RMJM/1181069831
description: scientific article; zbMATH DE number 2144257