On differential equations in \(c\)-generalized functions
type: Item
instance of: scholarly article
title: On differential equations in \(c\)-generalized functions
zbMATH Open document ID: 0912.34009
author: V. Ya. Derr
author: K. I. Dizendorf
published in: Russian Mathematics
publication date: 1998-10-25T00:00:00Z
review text: Starting from the Cauchy problem for the linear differential equation \[ X'= B'(t)X+ F'(t),\quad t\in I, \] in the algebra of \(n\times n\) matrices over \(\mathbb{R}\), the authors are defining a very general notion of solutions to this problem in the class of Colombeau generalized functions. Properties of this type of solution and interesting examples are given. The classical Carathéodory notion of solution is included here.
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34A12
zbMATH DE Number: 1175173
zbMATH Keywords: distribution solutions
zbMATH Keywords: Cauchy problem
zbMATH Keywords: linear differential equation
zbMATH Keywords: Colombeau generalized functions
reviewed by: N. H. Pavel
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1175173