Distributed Delay Terms Research Articles

Global existence and exponential decay for a swelling porous-heat system subject to a distributed delay

In this article, we consider a swelling porous-heat system with viscous damping and distributed delay term. It’s well-known in the literature that the thermal effect only lacks exponential stability. For that, we need to add another damping mechanism to stabilize exponentially the system. However, we prove, based on the energy method, that the combination of viscous damping and thermal effect provokes an exponential stability in the presence of distributed delay irrespective of the wave speeds of the system.

Blow-up of solutions for a system of nonlocal singular viscoelastic equations with sources and distributed delay terms

In this paper, we investigate a scenario concerning a coupled nonlocal singular viscoelastic equation with sources and distributed delay terms. By establishing suitable conditions, we have proved that a finite-time blow-up occurs in the solution.

Exploring Thermoelastic Effects in Damped Bresse Systems with Distributed Delay

In this work, we consider the one-dimensional thermoelastic Bresse system by addressing the aspects of nonlinear damping and distributed delay term acting on the first and the second equations. We prove a stability result without the common assumption regarding wave speeds under Neumann boundary conditions. We discover a new relationship between the decay rate of the solution and the growth of ϖ at infinity. Our results were achieved using the multiplier method and the perturbed modified energy, named Lyapunov functions together with some properties of convex functions.

Decay rate of the solutions to the Cauchy problem of the Lord Shulman thermoelastic Timoshenko model with distributed delay

Abstract In this study, we address a Cauchy problem within the context of the one-dimensional Timoshenko system, incorporating a distributed delay term. The heat conduction aspect is described by the Lord-Shulman theory. Our demonstration establishes that the dissipation resulting from the coupling of the Timoshenko system with Lord-Shulman’s heat conduction is sufficiently robust to stabilize the system, albeit with a gradual decay rate. To support our findings, we convert the system into a first-order form and, utilizing the energy method in Fourier space, and derive point wise estimates for the Fourier transform of the solution. These estimates, in turn, provide evidence for the slow decay of the solution.

Well-posedness and general energy decay for a nonlinear piezoelectric beams system with magnetic and thermal effects in the presence of distributed delay

In this paper, we consider one-dimensional nonlinear piezoelectric beams with thermal and magnetic effects in the presence of a distributed delay term acting on the heat equation. First, we show that the system is well-posed in the sense of a semigroup. Through the construction of an appropriate Lyapunov functional, we establish a general decay result for the solutions of the system, for which the exponential and polynomial decays are only special cases, under a suitable assumption on the weight of the delay that the damping effect through heat conduction is strong enough to stabilize the system even in the presence of a time delay. Furthermore, our result does not depend on any relationship between system parameters.

Oscillatory Behavior of the Solutions for a Parkinson’s Disease Model with Discrete and Distributed Delays

In this paper, the oscillatory behavior of the solutions for a Parkinson’s disease model with discrete and distributed delays is discussed. The distributed delay terms can be changed to new functions such that the original model is equivalent to a system in which it only has discrete delays. Using Taylor’s expansion, the system can be linearized at the equilibrium to obtain both the linearized part and the nonlinearized part. One can see that the nonlinearized part is a disturbed term of the system. Therefore, the instability of the linearized system implies the instability of the whole system. If a system is unstable for a small delay, then the instability of this system will be maintained as the delay increased. By analyzing the linearized system at the smallest delay, some sufficient conditions to guarantee the existence of oscillatory solutions for a delayed Parkinson’s disease system can be obtained. It is found that under suitable conditions on the parameters, time delay affects the stability of the system. The present method does not need to consider a bifurcating equation. Some numerical simulations are provided to illustrate the theoretical result.

Growth of solutions for a system of nonlocal singular viscoelastic equation with sources and distributed delay terms

Growth of solutions for a system of nonlocal singular viscoelastic equation with sources and distributed delay terms

Stabilization of a microbeam system with a boundary or internal distributed delay

In this paper, we consider the microbeam system with distributed delay term on the boundary or into the domain. In both cases, and thanks to a clever combination of spectral decomposition theory of Sz-Nagy-Foias [18] and frequency domain approach and under some additional and suitable assumptions, we prove the exponential stability of the total energy of our considered system.

Stability result for Lord Shulman swelling porous thermo-elastic soils with distributed delay term

Abstract The Lord Shulman swelling porous thermo-elastic soil system with the presence of a distributed delay term is studied in this work. We will establish the well-posedness of the system and the exponential stability of the system is derived.

Exponential stability of Lord Shulman thermoelastic system with porous damping and distributed delay term

In this paper, we consider a one-dimensional Lord–Shulman thermoelastic system [C. Cattaneo, On a form of heat equation which eliminates the paradox of instantaneous propagation, C. R. Acad. Sci. Paris 247 (1958) 431–433] with porous damping and distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well posedness of the system by using semigroup theory and we show that the dissipations due to thermal effects with porous damping are strong enough to stabilise the system exponentially, independently of the wave speeds of the system.

Exponential stability for porous system of thermoelasticity-type III with past history and distributed delay term

As a continuity to the study by Ouchenane et al. [On the Porous-elastic system with thermoelasticity of type III and distributed delay: Well-posedness and stability, J. Funct. Spaces (2021) 1–12], we consider a one-dimensional linear thermoelastic system of porous type with past history and distributed delay term. This model deals with dynamics of engineering structures and non-classical problems of mathematical physics. It includes new results and their proofs with a help of the energy method combined with Lyapunov functional, we discuss the stability of system for the case of equal speeds of wave propagation.

Decay rate of the solutions to the Cauchy problem of the Bresse system in thermoelasticity of type III with distributed delay

The decay rate of solutions to a Bresse system in thermoelasticity of type III with respect to the distributed delay term is the subject of this study. We demonstrate our major finding utilising the energy approach in the Fourier space.

Exponential Stability for Damped Shear Beam Model and New Facts Related to the Classical Timoshenko System With a Distributed Delay Term

We consider in this manuscript  a Timoshenko type beam model with a distributed delay term.  If the distributed delay term is small enough, we prove the global existence of solutions by using the Faedo-Galerkin approximations together with some energy estimates. Under suitable assumptions, we prove exponential stability of the solution. This result is obtained by introducing a suitable Lyapounov function.

Global Well-posedness and exponentail stability results for Bresse Timoshenko type systems of second sound with distributed delay term

Global Well-posedness and exponentail stability results for Bresse Timoshenko type systems of second sound with distributed delay term

Sampled Memory-Event-Triggered Fuzzy Load Frequency Control for Wind Power Systems Subject to Outliers and Transmission Delays.

This study is devoted to event-triggered fuzzy load frequency control (LFC) for wind power systems (WPSs) with measurement outliers and transmission delays. Due to the integration of wind turbine (WT) with nonlinearity, the T-S fuzzy model of WPS is established for stability analysis and controller design. To mitigate the network burden, a new sampled memory-event-triggered mechanism (SMETM) related to historical system information is presented. It has the following two merits: 1) the utilization of continuous memory outputs over a given interval is useful to reduce the information loss in the period of samples and the redundant triggering events induced by disturbances and noises and 2) an extra upper constraint is added in the triggering condition to generate a new event only when the error signal belongs to a bounded range, thus, the false events caused by measurement outliers can be differentiated out and then be dropped. By representing the memory signal with transmission delay as a time-varying distributed delay term, a T-S fuzzy time-varying distributed delay system is built up to model the H∞ LFC WPS. With the help of the Lyapunov method and the integral inequality relying on distributed delay, some criteria are derived to solve the triggering matrix and fuzzy controllers. Finally, the merits of the proposed SMETM are tested by simulation results.

A Stability Result for a Timoshenko System with Infinite History and Distributed Delay Term

This manuscript is mainly focusing on a general stability of solution for one-dimensional Timoshenko system with infinite history and distributed delay term regardless also of the speeds of wave propagation. We prove our result by using the energy method combined with some properties of convex functions.

Existence and decay for the logarithmic Lamé system with internal distributed delay

In this work, we consider a logarithmic Lamé system with distributed delay term. Firstly, we study the well-posedness of solutions by using the semigroup theory. Then, we prove the solution of the Lamé system is uniformly bounded and global in time. Finally, we prove the decay of the solution. Our results are more general than the earlier results.

Identification of time delays in COVID-19 data

Abstract Objective COVID-19 data released by public health authorities is subject to inherent time delays. Such delays have many causes, including delays in data reporting and the natural incubation period of the disease. We develop and introduce a numerical procedure to recover the distribution of these delays from data. Methods We extend a previously-introduced compartmental model with a nonlinear, distributed-delay term with a general distribution, obtaining an integrodifferential equation. We show this model can be approximated by a weighted-sum of constant time-delay terms, yielding a linear problem for the distribution weights. Standard optimization can then be used to recover the weights, approximating the distribution of the time delays. We demonstrate the viability of the approach against data from Italy and Austria. Results We find that the delay-distributions for both Italy and Austria follow a Gaussian-like profile, with a mean of around 11 to 14 days. However, we note that the delay does not appear constant across all data types, with infection, recovery, and mortality data showing slightly different trends, suggesting the presence of independent delays in each of these processes. We also found that the recovered delay-distribution is not sensitive to the discretization resolution. Conclusions These results establish the validity of the introduced procedure for the identification of time-delays in COVID-19 data. Our methods are not limited to COVID-19, and may be applied to other types of epidemiological data, or indeed any dynamical system with time-delay effects.

Polynomial stability of a transmission problem with second sound and distributed delay term

Polynomial stability of a transmission problem with second sound and distributed delay term

Control of Multi-Agent Systems with Distributed Delay

This study deals with the control of nonlinear multi-agent systems in which the interconnections among the agents can be modeled using distributed delay terms. It was shown that in the addressed multi-agent system class, the stabilization of the agent outputs can be performed with a prescribed precision. The proposed decentralized control approach combines passivity-based control, the synchronization of dynamic systems, and delay systems theory to achieve the control goal. As an application, the control of single-species migration networks with distributed delay was addressed. The setpoint control problem in such networks can be solved by extending the proposed passivity-based control with a suitably chosen feed-forward term. Simulation results are also provided to show the applicability of the proposed control strategy.