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A domain of influence in the Moore–Gibson–Thompson theory of dipolar bodies
Journal of Taibah University for Science ( IF 3.3 ) Pub Date : 2020-05-12 , DOI: 10.1080/16583655.2020.1763664
M. Marin 1 , M. I. A. Othman 2 , A. R. Seadawy 3 , C. Carstea 4
Affiliation  

We establish a domain of influence theorem for the mixed initial-boundary value problem in the context of the Moore–Gibson–Thompson theory of thermoelasticity for dipolar bodies. Based on the data of the mixed problem, we define, for a finite time t>0, a bounded domain Bt and prove that the displacements and the temperature decrease to zero, outside of the domain Bt. The main result is obtained with the help of two auxiliary results, namely two integral inequalities. We managed to prove that this type of influence domain can be built even if it is considered in a much more complex context. Thus, compared to the classical context in which this concept appeared, we took into account the heat conduction principle from the Moore–Gibson–Thompson theory, we considered the thermal effect and we analyzed the effect of the dipolar structure of the environment.



中文翻译:

偶极体的摩尔–吉布森–汤普森理论中的影响域

我们在偶极子热弹性的摩尔–吉布森–汤普森热力学理论的背景下,建立了混合初边值问题的影响定理的域。根据混合问题的数据,我们在有限时间t > 0内定义一个有界域Ť 并证明在域外位移和温度降为零 Ť。借助于两个辅助结果,即两个积分不等式,获得了主要结果。我们设法证明,即使在更复杂的环境中考虑,也可以建立这种影响范围。因此,与出现该概念的经典环境相比,我们考虑了Moore–Gibson–Thompson理论的热传导原理,考虑了热效应,并分析了环境的偶极结构的效应。

更新日期:2020-05-12
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