An algebra of distributions and generalized solutions to nonlinear equations
type: Item
instance of: scholarly article
title: An algebra of distributions and generalized solutions to nonlinear equations
zbMATH Open document ID: 0892.46040
published in: Doklady Mathematics
publication date: 1998-07-20T00:00:00Z
review text: In recent years, several works have considered generalized solutions to nonlinear differential equations. This problem eventually reduces to the multiplication of distributions. The known multiplication theory of Colombeau is convenient for proving existence theorems and using numerical methods, but it is not very constructive because the products of distributions are no longer functionals, which does not allow solutions to equations to be represented in an acceptable form. In this paper a method of finding generalized solutions to nonlinear equations, which is an analog of the method of undetermined coefficients for linear differential equations, is demonstrated.
Mathematics Subject Classification ID: 46F10
Mathematics Subject Classification ID: 47E05
zbMATH DE Number: 1037719
zbMATH Keywords: generalized solutions to nonlinear differential equations
zbMATH Keywords: multiplication of distributions
zbMATH Keywords: method of undetermined coefficients
author: V. M. Shelkovich
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1037719