Travelling wave solutions to some PDEs of mathematical physics
type: Item
instance of: scholarly article
title: Travelling wave solutions to some PDEs of mathematical physics
zbMATH Open document ID: 1069.35057
DOI: 10.1155/S0161171204108028
author: Kourosh Nozari
author: Ghasem A. Afrouzi
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51560
review text: Summary: Nonlinear operations such as multiplication of distributions are not allowed in the classical theory of distributions. As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity and multifluid flows, or some new cosmological models such as signature changing space-times. Colombeau's new theory of generalized functions can be used to remove these ambiguities. In this paper, we first consider a simplified model of elasticity and multifluid flows in the framework of Colombeau's theory and show how one can handle such problems, investigate their jump conditions, and resolve their ambiguities. Then we consider as a new proposal the case of cosmological models with signature change and use Colombeau's theory to solve the Einstein equation for the beginning of the universe.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 35Q72
Mathematics Subject Classification ID: 46F30
Mathematics Subject Classification ID: 83C05
zbMATH DE Number: 2168668
zbMATH Keywords: equations such as differential equations of elasticity and multifluid flows
zbMATH Keywords: signature changing space-times
zbMATH Keywords: Einstein equation
zbMATH Keywords: Colombeau generalized functions
zbMATH Keywords: Colombeau algebra
zbMATH Keywords: cosmological models
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2168668