Matrix Fourier transforms for consistent mathematical models
type: Item
instance of: scholarly article
title: Matrix Fourier transforms for consistent mathematical models
zbMATH Open document ID: 1367.42006
DOI: 10.1155/2016/1975493
author: Natalia Yaremko
author: O. E. Yaremko
published in: Chinese Journal of Mathematics
publication date: 2017-04-21T00:00:00Z
review text: Summary: We create a matrix integral transforms method; it allows us to describe analytically the consistent mathematical models. An explicit constructions for direct and inverse Fourier matrix transforms with discontinuous coefficients are established. We introduce special types of Fourier matrix transforms: matrix cosine transforms, matrix sine transforms, and matrix transforms with piecewise trigonometric kernels. The integral transforms of such kinds are used for problems solving of mathematical physics in homogeneous and piecewise homogeneous media. Analytical solution of iterated heat conduction equation is obtained. Stress produced in the elastic semi-infinite solid by pressure is obtained in the integral form.
Mathematics Subject Classification ID: 42B10
Mathematics Subject Classification ID: 35Q74
Mathematics Subject Classification ID: 74B10
Mathematics Subject Classification ID: 35Q79
zbMATH DE Number: 6707026
zbMATH Keywords: Fourier matrix transforms with discontinuous coefficients
zbMATH Keywords: piecewise trigonometric kernels
zbMATH Keywords: piecewise homogeneous media
zbMATH Keywords: heat conduction equation
zbMATH Keywords: elastic semi-infinite solid
Wikidata QID: Q59123286
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/1975493
OpenAlex ID: W2508133515
cites work: Q5528042
cites work: Q3254327
cites work: Q3531572
cites work: Q3159056
cites work: Fourier Inversion for Piecewise Smooth Functions in Several Variables
cites work: Q4393445
cites work: Fourier Transform Applications
cites work: Q4800024
cites work: Q3088206
description: scientific article; zbMATH DE number 6707026