Vanishing waves on closed intervals and propagating short-range phenomena
type: Item
instance of: scholarly article
title: Vanishing waves on closed intervals and propagating short-range phenomena
zbMATH Open document ID: 1177.35022
DOI: 10.1155/2008/359481
author: Ghiocel Toma
author: Flavia Doboga
published in: Mathematical Problems in Engineering
publication date: 2009-06-11T00:00:00Z
full work available at URL: https://eudml.org/doc/45487
review text: Summary: This study presents mathematical aspects of wave equation considered on closed space intervals. It is shown that a solution of this equation can be represented by a certain superposition of traveling waves with null values for the amplitude and for the time derivatives of the resulting wave in the endpoints of this interval. Supplementary aspects connected with the possible existence of initial conditions for a second order differential system describing the amplitude of these localized oscillations are also studied, and requirements necessary for establishing a certain propagation direction for the wave (rejecting the possibility of reverse radiation) are also presented. Then it is shown that these aspects can be extended to a set of adjacent closed space intervals, by considering that a certain traveling wave propagating from an endpoint to the other can be defined on each space interval and a specific mathematical law (which can be approximated by a differential equation) describes the amplitude of these localized traveling waves as related to the space coordinates corresponding to the middle point of the interval. Using specific differential equations, it is shown that the existence of such propagating law for the amplitude of localized oscillations can generate periodical patterns and can explain fracture phenomena inside materials as well.
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35C05
zbMATH DE Number: 5564159
zbMATH Keywords: wave equation
zbMATH Keywords: travelling waves
zbMATH Keywords: propagating law
Wikidata QID: Q58646165
MaRDI profile type: Publication
OpenAlex ID: W2098979978
cites work: Computational Science - ICCS 2004
cites work: Q4330105
cites work: Q4886931
cites work: Q3418030
cites work: Wavelet and Wave Analysis as Applied to Materials with Micro or Nanostructure
description: scientific article; zbMATH DE number 5564159