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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
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 |
| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |