General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay

Limam, Abdelaziz; Boukhatem, Yamna; Benabderrahmane, Benyattou

doi:10.15407/mag17.02.175

Cited by 3 publications

(8 citation statements)

References 34 publications

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“…Under a wider class of generality of relaxation functions, we establish the general decay rates by constructing a suitable Lyapunov functional. This paper extends the system studied by Limam et al [26] in the case of infinite memory.…”

Section: Introductionsupporting

confidence: 67%

“…Proof. The functions 𝐾 𝑖 , 𝑖 = 1, … , 4; are estimated as follows (see [26]), for 0 < 𝛼 < 1 and 𝛿 > 0, for all 𝑡 ≥ 0 where 𝐶 𝑖 , 𝑖 = 1, …, 13; are positive constants and…”

Section: Lemma 41 the Energy Functional (42) Along The Solution Of Eq...mentioning

confidence: 99%

“…They rated the heat conduction of type III in which has been of dissipative nature, where the heat flux is a combination of type I and II as limiting cases. Many works were devoted to investigate the existence, uniqueness, and asymptotic stability of solutions of thermoelastic systems, see [10,26,27,29,36], and references therein.…”

Section: Introductionmentioning

confidence: 99%

“…For the Neumann damped condition overfull the boundary in Equation (1.8), Cavalcanti et al [12] showed general existence and stability results by applying essentially the same technique as in [25] that are based on a natural tool for the problem-monotone operator theory. For some results concerning stability/instability results, as well as weak solutions of wave equations with discrete/distributed delay, we recall the reader to [9,17,26,33].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Global solvability and decay estimates for a type III thermo‐viscoelastic coupled system with infinite memory and boundary interaction feedback

Limam

Boukhatem

Benabderrahmane

2023

Mathematische Nachrichten

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A type III thermo‐viscoelastic coupled system with infinite memory and distributed delay is considered. The interaction feedback between the nonlinear damping and the acoustic conditions are reacted on portion of the boundary. We obtain the well posedness and regularity of the system by using semigroup theory which is combined with Schauder's fixed point theorem. Moreover, the general decay estimates are established under a much larger class of relaxation functions. Our results are obtained without the boundedness condition of initial data assumed in many earlier papers in the literature. This work generalizes the composite stability between infinite memory and nonlinear damping.

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Section: Introductionsupporting

confidence: 67%

Section: Lemma 41 the Energy Functional (42) Along The Solution Of Eq...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Global solvability and decay estimates for a type III thermo‐viscoelastic coupled system with infinite memory and boundary interaction feedback

Limam

Boukhatem

Benabderrahmane

2023

Mathematische Nachrichten

Self Cite

View full text Add to dashboard Cite

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“…Scholars such as Limam A proposed an enhanced faulty node detection method using interval weighting factors, which uses pseudo-random BCH codes for distributed network control systems to monitor node behavior, and the master node collects the single-bit BCH of each slave node. The replacement of the cyclic redundancy check CRC code by the code, this scheme can be used to detect and prevent serious damage caused by node failure [5]. Although there are many researches on multi-task scheduling and coupled distributed systems, there are few studies on coupled distributed systems considering multi-task dynamic scheduling.…”

Section: Introductionmentioning

confidence: 99%

Coupled Distributed Systems Considering Multitasking Dynamic Scheduling Algorithms

2021

DPS

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With the rapid development of Internet technology and the comprehensive arrival of the era of big data, the development of enterprise business scale and the rise of logic complexity make coupled distributed systems play an increasingly important role in enterprise-level applications. The multi-task dynamic scheduling scheme based on the proposed method has problems such as poor manageability, poor task scheduling ability and poor usability. Therefore, this paper studies and constructs the coupled distributed system considering the multi-task dynamic scheduling. This paper firstly introduces the relevant theories. In the system theory part, it mainly introduces the scheduling module, followed by the system design. In the system design part, the task scheduling is mainly designed. Finally, the system implementation is carried out. Scheduling accuracy is analyzed.

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Stability of thermoelastic diffusion problem of type III in spaces of different dimensions

2023

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In this article, we study the stability issues of a thermoelastic diffusion problem of type III in spaces of different dimensions. First we prove that the onedimensional problem is exponentially stable without adding damping terms.Then we prove the lack of exponential stability in the two-dimensional space. Moreover, a frictional damping for the elastic component leads to the exponential stability in three-dimensional space. As the form of the damping term depends on the nature of the material, we will distinguish the case of isotropic materials and the case of anisotropic materials.

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General Decay Result for a Type III Thermoelastic Coupled System with Acoustic Boundary Conditions in the Presence of Distributed Delay

Cited by 3 publications

References 34 publications

Global solvability and decay estimates for a type III thermo‐viscoelastic coupled system with infinite memory and boundary interaction feedback

Global solvability and decay estimates for a type III thermo‐viscoelastic coupled system with infinite memory and boundary interaction feedback

Coupled Distributed Systems Considering Multitasking Dynamic Scheduling Algorithms

Stability of thermoelastic diffusion problem of type III in spaces of different dimensions

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