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It is seen how to write the standard\^E form of the four partial differential equations in four unknowns of anisotropic thermoelasticity as a single equation in one variable, in terms of isothermal and isentropic wave operators. This…

Classical Physics · Physics 2020-05-11 N. H. Scott

The presence of a delay in a thermoelastic system destroys the well-posedness and the stabilizing effect of the heat conduction [17]. To avoid this problem we add to the system, at the delayed equation, a Kelvin-Voigt damping. At first, we…

Analysis of PDEs · Mathematics 2020-12-23 Smain Monlay Khatir , Farhat Shel

This paper studies the stability of an abstract thermoelastic system with Cattaneo's law, which describes finite heat propagation speed in a medium. We introduce a region of parameters containing coupling, thermal dissipation, and possible…

Analysis of PDEs · Mathematics 2024-09-23 Chenxi Deng , Zhong-Jie Han , Zhaobin Kuang , Qiong Zhang

Some uniform decay estimates are established for solutions of the following type of retarded integral inequalities: $$y(t)\leq E(t,\tau)||y_\tau||+\int_\tau^t K_1(t,s)||y_s||ds+\int_t^\infty K_2(t,s)||y_s||ds+\rho, \hspace{0.5cm}…

Dynamical Systems · Mathematics 2020-08-18 Desheng Li , Qiang Liu , Xuewei Ju

Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…

Dynamical Systems · Mathematics 2025-08-25 Quinlan Leishman , Benjamin Webb

We consider a linear scalar delay differential equation (DDE), consisting of two arbitrary distributed time delays. We formulate necessary conditions for stability of the trivial solution which are independent of the distributions. For the…

Dynamical Systems · Mathematics 2017-02-03 Sue Ann Campbell , Israel Ncube

We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…

Dynamical Systems · Mathematics 2019-02-21 Elena Braverman , Basak Karpuz

Within this paper, we introduce partially and fully decoupled time stepping schemes for linear thermo-poroelasticity. This means that the mechanics, heat, and flow equations can be solved sequentially. We provide sufficient conditions on…

Numerical Analysis · Mathematics 2026-03-17 R. Altmann , R. Maier , J. Schmeck

In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…

Dynamical Systems · Mathematics 2024-05-28 Javad A. Asadzade , Nazim I. Mahmudov

This manuscript is concerned with the one-dimensional system \[ \begin{array}{l} \tau u_{ttt} + \alpha u_{tt} = b \big(\gamma(\Theta) u_{xt}\big)_x + \big( \gamma(\Theta) u_x\big)_x, \\[1mm] \Theta_t = D \Theta_{xx} + b\gamma(\Theta)…

Analysis of PDEs · Mathematics 2026-02-13 Tobias Black , Michael Winkler

Boundary element methods provide powerful techniques for the analysis of problems involving coupled multi-physical response, especially in the linear case for which boundary-only formulations are possible. This paper presents the integral…

Classical Physics · Physics 2017-04-11 Ali R. Hadjesfandiari , Arezoo Hajesfandiari , Gary F. Dargush

We construct stable periodic solutions for a simple form nonlinear delay differential equation (DDE) with a periodic coefficient. The equation involves one underlying nonlinearity with the multiplicative periodic coefficient. The well-known…

Dynamical Systems · Mathematics 2024-02-14 Anatoli Ivanov , Sergiy Shelyag

The main aim of this paper is the investigation of the stability problem for ordinary delay differential equations. More precisely, we would like to study the following problem. Assume that for a continuous function a given delay…

Classical Analysis and ODEs · Mathematics 2016-12-01 Eszter Gselmann , Anna Kelemen

This paper continues the study of [11, 13] for stationary solutions of stochastic linear retarded functional differential equations with the emphasis on delays which appear in those terms including spatial partial derivatives. As a…

Probability · Mathematics 2014-02-11 Kai Liu

We study the asymptotic behavior of the solutions of the time-delayed higher-order dispersive nonlinear differential equation \begin{equation*} u_t(x,t)+Au(x,t) +\lambda_0(x) u(x,t)+\lambda(x) u(x,t-\tau )=0 \end{equation*} where…

Analysis of PDEs · Mathematics 2025-09-15 Roberto de A. Capistrano Filho , Fernando Gallego , Vilmos Komornik

This paper investigates the stability properties of a nonlinear fractional differential equation with two discrete delays and a delay-dependent coefficient. Such equations arise in various biological and control systems where temporal…

Dynamical Systems · Mathematics 2026-03-12 Pragati Dutta , Sachin Bhalekar

In this work, we consider the existence of global solution and the exponential decay of a nonlinear porous elastic system with time delay. The nonlinear term as well as the delay acting in the equation of the volume fraction. In order to…

Analysis of PDEs · Mathematics 2023-06-22 M. J. Dos Santos , C. A. Raposo , L. G. R. Miranda , B. Feng

In this paper we consider a nonlinear Petrovsky equation in a bounded domain with a delay term and a strong dissipation \begin{align*} u_{tt} + \Delta^{2} u -\mu_1g_1( \Delta( u_t(x,t))) -\mu_2g_2( \Delta (u_t(x,t-\tau))) =0. \end{align*}…

Analysis of PDEs · Mathematics 2021-08-20 Ahmed Chahtou , Mama Abdelli , Akram Ben Aissa

The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…

Dynamical Systems · Mathematics 2020-05-13 Phi Ha

In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…

Probability · Mathematics 2017-07-26 Kai Liu