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...
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| Format: | Article |
| Language: | English |
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Wiley
2015-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/2015/479267 |
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| author | Denys Ya. Khusainov Michael Pokojovy |
| author_facet | Denys Ya. Khusainov Michael Pokojovy |
| author_sort | Denys Ya. Khusainov |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-14d42d9016aa49089838aa0de35b3334 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2015-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-14d42d9016aa49089838aa0de35b33342025-02-03T01:23:54ZengWileyInternational 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 |
| spellingShingle | Denys Ya. Khusainov Michael Pokojovy Solving the Linear 1D Thermoelasticity Equations with Pure Delay International Journal of Mathematics and Mathematical Sciences |
| title | 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_short | Solving the Linear 1D Thermoelasticity Equations with Pure Delay |
| title_sort | solving the linear 1d thermoelasticity equations with pure delay |
| url | http://dx.doi.org/10.1155/2015/479267 |
| work_keys_str_mv | AT denysyakhusainov solvingthelinear1dthermoelasticityequationswithpuredelay AT michaelpokojovy solvingthelinear1dthermoelasticityequationswithpuredelay |