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General stability of abstract thermoelastic system with infinite memory and delay
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2020-10-21 , DOI: 10.3934/mcrf.2020040 Jianghao Hao , , Junna Zhang
Mathematical Control and Related Fields ( IF 1.2 ) Pub Date : 2020-10-21 , DOI: 10.3934/mcrf.2020040 Jianghao Hao , , Junna Zhang
In this paper we study an abstract thermoelastic system in Hilbert space with infinite memory and time delay. Under some suitable conditions, we prove the well-posedness by invoking semigroup theory. Since the damping may stabilize the system while the delay may destabilize it, we discuss the interaction between the damping and the delay term, and obtain that the system is uniformly stable when the effect of damping is greater than that of time delay. By establishing suitable Lyapunov functionals which are equivalent to the energy of system we also establish the general energy decay results for abstract thermoelastic system.
中文翻译:
具有无限记忆和时滞的抽象热弹性系统的一般稳定性
在本文中,我们研究了希尔伯特空间中具有无限存储和时滞的抽象热弹性系统。在一些合适的条件下,我们通过调用半群理论证明了适定性。由于阻尼可以使系统稳定,而延迟可能会使系统不稳定,因此,我们讨论了阻尼和延迟项之间的相互作用,并且当阻尼的影响大于时间延迟时,系统将保持稳定。通过建立适合于系统能量的Lyapunov泛函,我们还建立了抽象热弹性系统的一般能量衰减结果。
更新日期:2020-10-21
中文翻译:
具有无限记忆和时滞的抽象热弹性系统的一般稳定性
在本文中,我们研究了希尔伯特空间中具有无限存储和时滞的抽象热弹性系统。在一些合适的条件下,我们通过调用半群理论证明了适定性。由于阻尼可以使系统稳定,而延迟可能会使系统不稳定,因此,我们讨论了阻尼和延迟项之间的相互作用,并且当阻尼的影响大于时间延迟时,系统将保持稳定。通过建立适合于系统能量的Lyapunov泛函,我们还建立了抽象热弹性系统的一般能量衰减结果。