Thermoelastic System Research Articles

On well-posedness and exponential decay of swelling porous thermoelastic media with second sound

This work focuses on the well-posedness and exponential stability results of a swelling porous thermoelastic system with heat flux given by Maxwell-Cattaneo's law. Precisely, using the well-known Lumer-Phillips theorem, we establish the well-posedness result of the system. Furthermore, using the multiplier method, we prove that the system is exponential stable irrespective of any stability number or equality of wave propagation. This result is unique and unexpected, especially when compared to similar problems like Timoshenko, Bresse, and thermoelasticity with second sound. In each of the systems mentioned above, a stability number is necessary for the exponential stability of the systems. Undoubtedly, our coupling and the result give new contributions to the asymptotic behaviors of swelling porous thermoelastic soils.

Uniform stabilisation of a thermoelastic system with static Wentzell conditions

In this paper, we consider a thermoelastic system with static Wentzell boundary conditions. We show the well-posedness, using the semigroup theory, and establish an explicit decay rate result, using the multiplier method. More precisely, we prove an exponential decay result under the influence of competing both boundary damping b u ′ and localised interior damping l ( x ) u ′ . Our method consists in establishing a crucial fundamental identity and exploiting it to derive the decay rates.

On the stability of recovering two sources and initial status in a stochastic hyperbolic-parabolic system

Consider an inverse problem of determining two stochastic source functions and the initial status simultaneously in a stochastic thermoelastic system, which is constituted of two stochastic equations of different types, namely a parabolic equation and a hyperbolic equation. To establish the conditional stability for such a coupling system in terms of some suitable norms revealing the stochastic property of the governed system, we first establish two Carleman estimates with regular weight function and two large parameters for stochastic parabolic equation and stochastic hyperbolic equation, respectively. By means of these two Carleman estimates, we finally prove the conditional stability for our inverse problem, provided the source in the elastic equation be known near the boundary and the solution be in an a priori bounded set. Due to the lack of information about the time derivative of wave field at the final time, the stability index with respect to the wave field at final time is found to be halved, which reveals the special characteristic of our inverse problem for the coupling system.

General stabilization of a thermoelastic systems with a boundary control of a memory type

"In this paper we consider an n-dimensional thermoelastic system, in a bounded domain, where the memory-type damping is acting on a part of the boundary and where the resolvent kernel k of ${-g^{\prime }(t)}/{g(0)} $ satisfies\linebreak $k^{\prime \prime }(t)\geq \gamma \left( t\right) (-k^{\prime }(t))^{p}$, $t\geq 0$, $1< p<\frac{3}{2} $. We establish a general decay result, from which the usual exponential and polynomial decay rates are only special cases. This work generalizes and improves earlier results in the literature."

Exponential stability of Timoshenko system in thermoelasticity of second sound with a memory and distributed delay term

Abstract 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.

Thermoelastic Timoshenko system free of second spectrum

In this work we prove the well-posedness and establish the uniform stability of a thermoelastic Timoshenko system free of second spectrum. The heat conduction is governed by classical Fourier’s law. Our stability result holds for any parameters of the system.

Weighted Hardy–Sobolev inequality and global existence result of thermoelastic system on manifolds with corner‐edge singularities

This article concerns with the thermoelastic corner‐edge‐type system with singular potential function on a wedge manifold with corner singularities. First, we introduce weighted p‐Sobolev spaces on manifolds with corner‐edge singularities. Then, we prove the corner‐edge‐type Sobolev inequality, Poincar inequality and Hardy inequality and obtain some results about the compactness of embedding maps on the weighted corner‐edge Sobolev spaces. Finally, as an application of these results, we apply the potential well theory and the Faedo–Galerkin approximations to obtain the global weak solutions for the thermoelastic corner‐edge‐type system 1.1.

Dynamics of a new thermoelastic Timoshenko system with second sound

This work studies the optimal and general stability of a thermoelastic Timoshenko system with second sound. More succinctly, under some assumptions on the parameters of the system, we derive an optimal and general decay result for the solution energy of a thermoelastic Timoshenko system in which there is viscoelasticity in the transverse displacement. Examples are given to show that, polynomial and exponential decay rates are particular cases.

General stability result for a porous thermoelastic system with infinite history and microtemperatures effects

In this paper, we consider a one‐dimensional porous thermoelastic system with microtemperatures effects and past history term acting only on the porous equation. We show that the system is well‐posed in the sens of semigroup and based on the energy method we establish a general decay result for the solutions of the system under an appropriate assumptions on the kernel. Furthermore, our result does not depend on any relationship between the coefficients of the system. The result of this paper improves some results in the literature.

Riemann problem of (λ, k) bi-analytic functions

A kind of Riemann problem of bi-analytic functions are studied by using the theory of boundary value problems for analytic functions. The solutions of Riemann problem of bi-analytic function are obtained. The conclusion may be applied to the quasi-static system of thermoelasticity.

Long-time behaviour of a translational thermoelastic Timoshenko system with second sound

We consider a Timoshenko system coupled with heat equations modelled by Cattaneo's law. The coupling is through the transverse displacement. Both ends of the beam are dynamic. One end of the beam is fixed to a base in a translational motion and a tip mass is attached to the other end. We design a feedback control acting at the base. It is shown that this feedback control is a reasonable one and is capable of stabilizing the system. We prove an exponential and a polynomial stability result using the multiplier technique. To this end, we introduce new functionals to form a suitable Lyapunov functional.

Exponential stability of a porous thermoelastic system with Gurtin–Pipkin thermal law

Exponential stability of a porous thermoelastic system with Gurtin–Pipkin thermal law

General decay for a viscoelastic-type Timoshenko system with thermoelasticity of type III

We consider a one-dimensional thermoelastic Timoshenko system, where the heat conduction is given by Green and Naghdi theories and acting on shear force. We prove that the unique damping given by the memory is sufficiently strong to stabilize the system exponentially, depending on a new relationship between the coefficients of the system and under some assumptions on the kernel of the memory term. In fact, we establish a general decay result, of which exponential and polynomial decay results are special cases.

A new stability result for a thermoelastic Bresse system with viscoelastic damping

We investigate a thermoelastic Bresse system with viscoelastic damping acting on the shear force and heat conduction acting on the bending moment. We show that with weaker conditions on the relaxation function and physical parameters, the solution energy has general and optimal decay rates. Some examples are given to illustrate the findings.

Gradient-dependent heat rectification in thermoelastic solids

We study heat rectification by means of application of an inhomogeneous distribution of a tensile mechanical stress in: (a) graded thermoelastic systems with constant cross section; (b) non-graded thermoelastic systems with variable cross section. In both cases the thermal conductivity of the material may be partially tuned by the internal strain produced by the application of transversal mechanical stress. We calculate the rectification coefficient as function of different control parameters, such as applied strain, stoichiometry, geometry, external heat flux. In the case (a) we consider three different graduations in the case (b) three different internal strain distributions with L 1 the length of the system and 0 a constant strain. In both cases we show that, the higher n, the higher the rectification coefficient. We have also considered how the rectification depends on 0, whose value may be easily controlled from the outside, thus allowing some degree of control on the rectification coefficient.

Global existence and blow-up for a thermoelastic system with p-Laplacian

In this paper, we study the following thermoelastic system with p-Laplacian in a bounded domain , where u and θ denote the elongation of a plate and the temperature difference to the equilibrium state, respectively; denotes the classical p-Laplacian operator. By employing the potential well theory, we discuss the properties of global existence and finite time blow-up for the solutions. Moreover, we give the lower and upper bounds of blow-up time to the blow-up solutions.

Asymptotic modeling of the behavior of a reinforced plate governed by a full von Karman thermo-elastic system with nonlinear thermal coupling

Asymptotic modeling of the behavior of a reinforced plate governed by a full von Karman thermo-elastic system with nonlinear thermal coupling

Exponential Stabilization of a Swelling Porous-Elastic System with Microtemperature Effect and Distributed Delay

The swelling porous thermoelastic system with the presence of temperatures, microtemperature effect, and distributed delay terms is considered. We will establish the well posedness of the system, and we prove the exponential stability result.

Thermoelastic problem in the setting of dual-phase-lag heat conduction: Existence and uniqueness of a weak solution

We investigate an isotropic thermoelastic system with dual-phase-lag heat conduction. We consider a homogeneous Dirichlet boundary condition for displacement and temperature. We formulate the variational formulation for the associated fully hyperbolic coupled system. By using a time discretization method, we show the existence of a unique weak solution under lower regularity assumptions on the data than established before in literature.

Forced Motions of Thermoelastic Systems of Memory Type

Forced Motions of Thermoelastic Systems of Memory Type