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In this paper, we consider a Bresse‐Timoshenko‐type system with distributed delay term. Under suitable assumptions, we establish the global well‐posedness of the initial and boundary value problem by using the Faedo‐Galerkin approximations and some energy estimates. By using the energy method, we show two exponential stability results for the system with delay in vertical displacement and in angular rotation, respectively. This extends earlier results in the literature. [ABSTRACT FROM AUTHOR]

Abstract In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 $f_{1}=f_{2}=0$ .

In this article, we focussed on a nonlinear viscoelastic Kirchhoff‐type equation with distributed delay and variable‐exponents. The blow‐up solutions of the problem are proved under suitable hypothesis, and by using an integral inequality due to Komornik, the general decay outcome is obtained in the case b=0$$ b=0 $$. [ABSTRACT FROM AUTHOR]

In this work, we consider a quasilinear system of viscoelastic equations with dispersion, source, distributed delay, and variable exponents. Under a suitable hypothesis the blow-up and growth of solutions are proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case of absence of the source term f 1 = f 2 = 0 . [ABSTRACT FROM AUTHOR]

Abstract We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up.

We examine a Kirchhoff-type equation with nonlinear viscoelastic properties, characterized by distributed delay, logarithmic nonlinearity, and Balakrishnan–Taylor damping terms (elastic membrane equation). Under appropriate hypotheses, we establish the occurrence of solution blow-up. [ABSTRACT FROM AUTHOR]

A nonlinear Kirchhoff-type equation with distributed delay and variableexponents is studied. Under suitable hypothesis the blow-up of solutions is proved, and by using an integral inequality due to Komornik the general decay result is obtained in the case b = 0. [ABSTRACT FROM AUTHOR]

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.

The Lord Shulman swelling porous thermo-elastic soil system with the effects of microtemperature, temperatures and distributed delay terms is considered in this study. The well-posedness result is established by the Lumer–Phillips corollary applied to the Hille–Yosida theorem. The exponential stability result is proven by the energy method under suitable assumptions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work, a nonlinear viscoelastic wave equation is studied. By supposing distributed delay feedback acting on the boundary, we establish the general decay rate under suitable hypothesis. [ABSTRACT FROM AUTHOR]

The subject of this research is a coupled system of nonlinear viscoelastic wave equations with distributed delay components, infinite memory and Balakrishnan-Taylor damping. Assume the kernels $ g_{i} :{\bf R}_{+}\rightarrow {\bf R}_{+} $ holds true the below $ g_{i}'(t)\leq-\zeta_{i}(t)G_{i}(g_{i}(t)), \quad \forall t\in {\bf R}_{+}, \quad {\rm{for}} \quad i = 1, 2, $ in which $ \zeta_{i} $ and $ G_{i} $ are functions. We demonstrate the stability of the system under this highly generic assumptions on the behaviour of $ g_i $ at infinity and by dropping the boundedness assumptions in the historical data.

The Lord Shulman swelling porous thermo-elastic soil system with the effects of microtemperature, temperatures and distributed delay terms is considered in this study. The well-posedness result is established by the Lumer–Phillips corollary applied to the Hille–Yosida theorem. The exponential stability result is proven by the energy method under suitable assumptions.

The subject of this research is a coupled system of nonlinear viscoelastic wave equations with distributed delay components, infinite memory and Balakrishnan-Taylor damping. Assume the kernels holds true the below in which and are functions. We demonstrate the stability of the system under this highly generic assumptions on the behaviour of at infinity and by dropping the boundedness assumptions in the historical data. [ABSTRACT FROM AUTHOR]

A nonlinear viscoelastic Kirchhoff-type equation with a logarithmic nonlinearity, Balakrishnan-Taylor damping, dispersion and distributed delay terms is studied. We establish the global existence of the solutions of the problem and by the energy method we prove an explicit and general decay rate result under suitable hypothesis.

Using the frequency domain approach, we prove the rational stability for a wave equation with distributed delay on the dynamical control, after establishing the strong stability and the lack of uniform stability.

This article concerns linear one-dimensional thermoelastic Timoshenko system with memory and distributed delay terms where the Cattaneo law governs the heat flux q(x,t)q\left(x,t). We proved an exponential stability result by using the energy method combined with Lyapunov functional.

A nonlinear viscoelastic wave equation with Balakrishnan-Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

In this paper, we study the well-posedness and the asymptotic behavior of a one-dimensional laminated beam system with a distributed delay term in the first equation, where the heat conduction is given by Fourier's law effective in the rotation angle displacements. We first give the well-posedness of the system by using the semigroup method. Then, we show that the system is exponentially stable under the assumption of equal wave speeds. [ABSTRACT FROM AUTHOR]

This work is concerned with a full von Kármán beam in the presence of infinite‐memory, microtemperature, and distributed delay terms. First, we establish the well posedness of the system. Second, we considered the kernel h:ℝ+→ℝ+ satisfying h(t)≤ξ(t)H(h(t)),∀t∈ℝ+,where ξ and H are functions satisfying some specific properties, and under this very general hypothesis on the behavior of h at infinity, we prove the stability of the system. [ABSTRACT FROM AUTHOR]

Abstract A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis.

In this article, our main concern is the study of the effect of a distributed time-delay in boundary stabilization of a strongly coupled multi-dimensional wave equations. We will establish that the system with time-delay inherits the same exponential decay rate from the corresponding one without delay. [ABSTRACT FROM AUTHOR]

As a continuity to the study by T. A. Apalara in [3], we consider a one-dimensional porous-elastic system with the presence of both memory and distributed delay terms in the second equation. Using the well known energy method combined with Lyapunov functionals approach, we prove a general decay result given in Theorem 2.1. [ABSTRACT FROM AUTHOR]

A nonlinear viscoelastic Kirchhoff-type equation with Balakrishnan–Taylor damping and distributed delay is studied. By the energy method we establish the general decay rate under suitable hypothesis. [ABSTRACT FROM AUTHOR]

Our main concern in this paper, is to prove the stability combined well-posedness results of solutions for a linear Timoshenko's beam laminated with thermoplastic and past history together with distributed delay terms for the both cases nonequal and equal speeds of wave propagation. By using of some of the usual basic theorems and well-known methods in functional analysis. [ABSTRACT FROM AUTHOR]

A longitudinal and transversal vibrations of the beam with nonlinear tension, a viscoelastic damping and distributed delay term is studied. Using the Faedo–Galerkin method, the well-posedness of the problem is established. A uniform decay result is proved by multiplier method. [ABSTRACT FROM AUTHOR]

In this paper, we consider a nonlinear viscoelastic Kirchhoff equation with the presence of both distributed delay term, Balakrishnan‐Taylor damping, and logarithmic nonlinearity. We describe a exponential decay of solutions, and we obtained the asymptotic stability result of the global solution. This study is a continuation of Boulaaras's works (Math. Meth. Appl. Sci. 2019;42:4795– 4814 and Alex. Eng. J. 2020;59:1059–1071) [ABSTRACT FROM AUTHOR]

In this paper, we consider a coupled Lame system with the presence of distributed delay term, viscoelastic, and logarithmic source terms. We describe an exponential decay of solutions, where an asymptotic stability result of global solution is obtained. This study is an extension to Boulaaras' work in Applicable Analysis (2019), 1–19. [ABSTRACT FROM AUTHOR]

In this work, we consider a linear thermoelastic laminated timoshenko beam with distributed delay, where the heat conduction is given by cattaneoâs law. we establish the well posedness of the system. For stability results, we prove exponential and polynomial stabilities of the system for the cases of equal and nonequal speeds of wave propagation. [ABSTRACT FROM AUTHOR]

In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation.

In the present paper, we consider an important problem from the application perspective in science and engineering, namely, one-dimensional porous–elastic systems with nonlinear damping, infinite memory and distributed delay terms. A new minimal conditions, placed on the nonlinear term and the relationship between the weights of the different damping mechanisms, are used to show the well-posedness of the solution using the semigroup theory. The solution energy has an explicit and optimal decay for the cases of equal and nonequal speeds of wave propagation. [ABSTRACT FROM AUTHOR]