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In this paper we consider a viscoelastic wave equation with a time-varying delay term, the coefficient of which is not necessarily positive. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we establish a…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
In this paper, we analyze an abstract thermoelastic system, where the heat conduction follows the Cattaneo law. Zero becomes a spectrum point of the system operator when the coupling and thermal damping parameters of system satisfy specific…
In this paper, we consider a viscoelastic kirchhoff equation with a delay term in the internal feedback. By using the Faedo-Galarkin approximation method we prove the well-posedness of the global solutions. Introducing suitable energy, we…
The goal of this paper is to study a nonlinear viscoelastic wave equation with strong damping, time-varying delay and dynamical boundary condition. By introducing suitable energy and Lyapunov functionals, under suitable assumptions, we then…
We consider a quasilinear PDE system which models nonlinear vibrations of a thermoelastic plate defined on a bounded domain in R^n. Well-posedness of solutions reconstructing maximal parabolic regularity in nonlinear thermoelastic plates is…
We consider the Cauchy problem of the viscous $\beta$-plane equations. We first establish the global well-posedness of the system for the initial data sufficiently small compared to the Rossby parameter. The smoothing effect of the flow is…
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…
In this article, we consider a vibrating nonlinear Timoshenko system with thermoelasticity with second sound. We discuss the well-posedness and the regularity of Timoshenko solution using the semi-group theory. Moreover, we etablish an…
This work is dedicated to the study of a linear model arising in thermoelastic rod of homogeneous material. The system is resulting from a coupling of a heat and a wave equation in the interval $(0,1)$ with Dirichlet boundary conditions at…
In this paper, we consider a transmission problem in a bounded domain with a viscoelastic term and a delay term. Under appropriate hypothesis on the relaxation function and the relationship between the weight of the damping and the weight…
A thermodynamically consistent visco-elastodynamical model at finite strains is derived that also allows for inelasticity (like plasticity or creep), thermal coupling, and poroelasticity with diffusion. The theory is developed in the…
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…
In this paper, we consider a stabilization problem of a generalized thermoelastic system (the so called $\alpha-\beta$ system) with delay in a part of the coupled system. For each case, we prove the well-posedness of the corresponding…
We consider a multilayer hyperbolic-parabolic PDE system which constitutes a coupling of 3D thermal - 2D elastic - 3D elastic dynamics, in which the boundary interface coupling between 3D fluid and 3D structure is realized via a 2D elastic…
In this paper, we consider a Timoshenko system with a thermo-viscoelastic damping and a delay term in the internal feedback together with initial datum and boundary conditions of Dirichlet type, where g is a positive non-increasing…
Within the framework of continuum mechanics, the full description Of joint motion of elastic bodies and compressible viscous fluids with taking into account thermal effects is given by the system consisting of the mass, momentum, and energy…
The thermodynamical model of viscoelastic deformable solids at finite strains with Kelvin-Voigt rheology with a higher-order viscosity (using the concept of multipolar materials) is formulated in a fully Eulerian way in rates. Assumptions…
As a first approach to the study of systems coupling finite and infinite dimensional natures, this article addresses the stability of a system of ordinary differential equations coupled with a classic heat equation using a Lyapunov…
Starting from the formal solution to the Heisenberg equation, we revisit an universal model for a quantum open system with a harmonic oscillator linearly coupled to a boson bath. The analysis of the decay process for a Fock state and a…