Solving the Linear 1D Thermoelasticity Equations with Pure Delay

Solving the Linear 1D Thermoelasticity Equations with Pure Delay

We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a cert...

Full description

Bibliographic Details
Main Authors: Denys Ya. Khusainov, Michael Pokojovy
Format: Article
Language:English
Published: Hindawi Limited 2015-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2015/479267
id doaj-14d42d9016aa49089838aa0de35b3334
record_format Article
spelling doaj-14d42d9016aa49089838aa0de35b33342020-11-24T21:11:46ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252015-01-01201510.1155/2015/479267479267Solving the Linear 1D Thermoelasticity Equations with Pure DelayDenys Ya. Khusainov0Michael Pokojovy1Department of Cybernetics, Kyiv National Taras Shevchenko University, 64 Volodymyrska Street, Kyiv 01601, UkraineDepartment of Mathematics and Statistics, University of Konstanz, Universitätsstraße 10, 78457 Konstanz, GermanyWe propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as τ→0. Finally, we deduce an explicit solution representation for the delay problem.http://dx.doi.org/10.1155/2015/479267
collection DOAJ
language English
format Article
sources DOAJ
author Denys Ya. Khusainov
Michael Pokojovy
spellingShingle Denys Ya. Khusainov
Michael Pokojovy
Solving the Linear 1D Thermoelasticity Equations with Pure Delay
International Journal of Mathematics and Mathematical Sciences
author_facet Denys Ya. Khusainov
Michael Pokojovy
author_sort Denys Ya. Khusainov
title Solving the Linear 1D Thermoelasticity Equations with Pure Delay
title_short Solving the Linear 1D Thermoelasticity Equations with Pure Delay
title_full Solving the Linear 1D Thermoelasticity Equations with Pure Delay
title_fullStr Solving the Linear 1D Thermoelasticity Equations with Pure Delay
title_full_unstemmed Solving the Linear 1D Thermoelasticity Equations with Pure Delay
title_sort solving the linear 1d thermoelasticity equations with pure delay
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2015-01-01
description We propose a system of partial differential equations with a single constant delay τ>0 describing the behavior of a one-dimensional thermoelastic solid occupying a bounded interval of R1. For an initial-boundary value problem associated with this system, we prove a well-posedness result in a certain topology under appropriate regularity conditions on the data. Further, we show the solution of our delayed model to converge to the solution of the classical equations of thermoelasticity as τ→0. Finally, we deduce an explicit solution representation for the delay problem.
url http://dx.doi.org/10.1155/2015/479267
work_keys_str_mv AT denysyakhusainov solvingthelinear1dthermoelasticityequationswithpuredelay
AT michaelpokojovy solvingthelinear1dthermoelasticityequationswithpuredelay
_version_ 1716752793112412160

Similar Items