In this paper we investigate the spatial behavior of the solutions for\uda theory for the heat conduction with one delay term. We obtain a Phragm én-\udLindelöf type alternative. That is, the solutions either decay in an exponential\udway or blow-up at in nity in an exponential way. We also show how to obtain\udan upper bound for the amplitude term. Later we point out how to extend\udthe results to a thermoelastic problem. We nish the paper by considering\udthe equation obtained by the Taylor approximation to the delay term. A\udPhragm én-Lindelöf type alternative is obtained for the forward and backward\udin time equations.
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机译：在本文中，我们研究了具有一个时滞项的热传导模型的解的空间行为。我们获得Phragmén-\udLindelöf类型的替代项。也就是说，解决方案要么以指数\ udway衰减，要么以指数方式爆炸。我们还展示了如何获得振幅项的\ udan上限。稍后我们指出如何将结果扩展到热弹性问题。我们通过考虑由泰勒逼近到延迟项的方程来整理论文。对于前向和后向\ udin时间方程式，获得了\\\\\\\\\\\\\\\\\\\\\\\\\，\\\\\\\\\\\\\\\ n \n-Lindelöf类型的替代方案。
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