Nonlinear maps in spaces of distributions
type: Item
instance of: scholarly article
title: Nonlinear maps in spaces of distributions
zbMATH Open document ID: 0729.46015
DOI: 10.1007/BF02570824
author: Todor Gramchev
published in: Mathematische Zeitschrift
publication date: 1992-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/174354
review text: One studies nonlinear superposition F(u) for certain strongly singular distributions u. It turns out that for analytic maps F(u) is a \(\sigma\)- ultradistribution and an effective link between the index \(\sigma\) and the strength of the singularity of u is established. An application to the Cauchy problems for a class of semilinear hyperbolic systems in space dimension one with singular initial data is proposed and construction of \(\sigma\)-Colombeau algebra is given.
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 46F05
zbMATH DE Number: 4205141
zbMATH Keywords: nonlinear superposition
zbMATH Keywords: strongly singular distributions
zbMATH Keywords: \(\sigma \) - ultradistribution
zbMATH Keywords: Cauchy problems for a class of semilinear hyperbolic systems in space dimension one with singular initial data
zbMATH Keywords: \(\sigma \) - Colombeau algebra
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4205141