Baowei Feng

Southwestern University of Finance and Economics · Department of Mathematics

This paper is concerned with long-time dynamics of laminated beams modeled from the well established Timoshenko system. Of particular interest is a model of two-layered beam proposed by Hansen and Spies which describes the slip effect produced by a thin adhesive layer uniting the structure. In a more general setting, involving a nonlinear foundatio...

In this paper we consider laminated beams modelled from the well established Timoshenko system, which is a structure given by two identical layers uniform on top of each other, taking into account that an adhesive of small thickness is bonding the two surfaces and produces an interfacial slip. By using semi-group approach, we prove the global well-...

(Accepted for publication) In this paper, a three-layer Rao-Nakra sandwich beam is considered where the core viscoelastic layer is constrained by the purely elastic or piezoelectric outer layers. In the model, uniform bending motions of the overall laminate are coupled to the longitudinal motions of the outer layers, and the shear of the middle lay...

This article studies the finite time blow-up of weak solutions to a structural acoustics model consisting of a semilinear wave equation defined on a bounded domain $\Omega\subset\mathbb{R}^3$ which is strongly coupled with a Berger plate equation acting on the elastic wall, namely, a flat portion of the boundary. The system is influenced by several...

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 obtain the existence and uniqueness of a global solution, we will use the semigroup theory of linear operators a...

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 obtain the existence and uniqueness of a global solution, we will use the semigroup theory of linear operators a...

In this paper, we consider a von Karman system with a linear memory term and a nonlinear boundary delay term. Thanks to a general condition on the relaxation function of the memory term, we are able to provide a general decay rate of the energy of the system. This outcome extends earlier results in the literature.

In this paper we consider a multi-dimensional Bresse with memory-type boundary conditions. By assuming minimal conditions on the resolvent kernel, we establish an optimal explicit and general energy decay result. This result is new and substantially improves earlier results in the literature.

In this paper, we consider a transmission problem for Kirchhoff‐type wave equations with boundary condition determined by the long‐range memory. The wave propagation over bodies consisting of two physically different types of materials. One component is clamped, and the other is in a viscoelastic fluid producing a dissipative mechanism on the bound...

In this paper we consider a model of laminated beams combining viscoelastic damping and strong time-delayed damping. The global well-posedness is proved by using the theory of semigroups of linear operators. We prove the lack of exponential stability when the speed wave propagations are not equal. In fact, we show in this situation, that the system...

In this paper, a piezoelectric beam is investigated under fully-dynamic magnetic effects and long-range dielectric and strain memories. The mathematical model under consideration is for the type of piezoelectric beams which strongly couple the electromagnetic effects with mechanical vibrations. This particular model is highly preferred for complex...

The nonuniform thermoelastic laminated beam of the Lord–Shulman type is considered. The model is a two‐layered beam with structural damping due to the interfacial slip. The well‐posedness is proved by the semigroup theory of linear operators approach together with the Lumer–Phillips theorem. The stability results presented in this paper depend on t...

In this paper we consider a laminated beam system with thermodiffusion effects with two kinds of boundary conditions, in which the mass diffusion introduces a new critical thickness in addition to the conventional critical thickness of thermoelastic damping. By using the method of semigroup, we prove the system is global well posed. The polynomial...

In this paper, a laminated beam system with two history-type controls is studied. One of the controls acts on the effective rotation angle and the other on the slip equation. The latter control replaces the structural damping usually considered in this model in the literature. Using the semigroup of linear operators approach, we prove the system is...

In this paper we study the well-posedness as well as the stabilization properties of the swelling porous elastic media with structural damping acting on both equations of the system. By using semigroup theory, we prove the system is globally well posed in energy space. We stablished the energy dissipation law since the classical relationship betwee...

This paper studies the long-time behavior of solutions for a transmission problem of Timoshenko beam with memory. We show that the stability of the system holds for a much larger class of relaxation functions and get better decay rate than the ones existing in the literature. We also give some numerical tests to validate the theoretical results.

In this paper, we investigate the decay properties of the unconstrained one dimensional suspension bridge model. With only partial damping acting on one or on both equations and with boundary dampings, we prove that the first order energy is decaying exponentially, our method of proof is based on the energy method to build the appropriate Lyapunov...

In this paper, we study the stability of a Bresse system with memory-type boundary conditions. For a wider class of kernel functions, we establish an optimal explicit energy decay result. Our stability result improves many earlier results in the literature. Finally, we also give four numerical tests to illustrate our theoretical results using the c...

In this paper, we investigate the decay properties of the thermoelastic Bresse system in the whole space. We consider many cases depending on the parameters of the model, and we establish new decay rates. We need to mention here that in some cases, we don't have the regularity‐loss phenomena as in the previous works in the literature. To prove our...

We consider an infinite-dimensional model for the longitudinal vibrations of a fully-dynamic piezoelectric beam which strongly couples mechanical vibrations and fully dynamic electromagnetic effects due to Maxwell's equations. The corresponding model is known to be not exponentially stabilizable by only one boundary feedback controller, controlling...

The main concern of this article is to investigate the stabilization problem of a flexible structure with one dynamical boundary condition subject to two nonlinearities in the proposed boundary control. Specifically, the first nonlinearity is related to the velocity term, while the second one arises from the delayed term. Despite such a situation,...

In this paper, we study the global well-posedness and exponential stability for a Rao-Nakra sandwich beam equation with time-varying weight and time-varying delay. The system consists of one Euler-Bernoulli beam equation for the transversal displacement, and two wave equations for the longitudinal displacements of the top and bottom layers. By usin...

This article concerns the long term behavior of solutions to a structural acoustic model consisting of a semilinear wave equation defined on a smooth bounded domain $\Omega\subset\mathbb{R}^3$ which is coupled with a Berger plate equation acting on a flat portion of the boundary of $\Omega$. The system is influenced by several competing forces, in...

In this paper, we investigate the decay properties of suspension bridge with memories in one dimension. To prove our results, we use the energy method to build some very delicate Lyapunov functionals that give the desired results.

In this paper, we consider a second-order abstract viscoelastic equation in Hilbert spaces with delay term in the nonlinear internal damping and a nonlinear source term. Under some suitable assumptions on the weight of the delayed feedback, the weight of the non-delayed feedback and the behavior of the relaxation function, we establish two explicit...

This paper deals with a nonlinear viscoelastic equation. The aim is to expand the class of the function of relaxation h(t) that ensuring a general decay. We adopt the following commonly condition on relaxation function h(t): h′(t)≤−ξ(t)χ(h(t)), where ξ is a nonincreasing function and χ is an increasing and convex function on the whole [0,∞) instead...

In this paper, we investigate the decay properties of the thermoelastic Timoshenko system with past history in the whole space where the thermal effects are given by Cattaneo and Fourier laws. We obtain that both systems, Timoshenko–Fourier and Timoshenko–Cattaneo, have the same rate of decay (1 + t)^{-1/4} and the regularity-loss-type property is...

This paper addresses the stabilization problem of a microscale beam system subject to a delay. Several situations are considered depending whether the delay occurs as a boundary or interior/distributed term. In both cases, the microbeam system is shown to be well posed in the sense of semigroups theory of linear operators. More importantly, using t...

In this paper, we investigate the decay properties of the thermoelastic Bresse system in the whole space. We consider many cases depending on the parameters of the model and we establish new decay rates. We need to mention here that, in some cases we don’t have the regularity-loss phenomena as in the previous works in the literature. To prove our r...

In this paper, we study the long-time dynamics of a system modelinga mixture of three interacting continua with nonlinear damping, sources terms and subjected to small perturbations of autonomousexternal forces with a parameter \begin{document}$ \epsilon $\end{document}, inspired by the modelstudied by Dell' Oro and Rivera [12]. We establish astabi...

In this paper, we study a Timoshenko system only with thermodiffusion effects. We establish exponential energy decay of the system with two kinds of boundary conditions under the assumption of the equal wave speeds. Our result extends the recent result by Aouadi et al. in Z. Angew. Math. Phys., 70, 117 (2019).

In this paper, we consider a Balakrishnan-Taylor viscoelastic wave equation with nonlinear frictional damping and logarithmic source term. By assuming a more general type of relaxation functions, we establish explicit and general decay rate results, using the multiplier method and some properties of the convex functions. This result is new and gene...

The stabilization properties of dissipative Timoshenko systems have been attracted the attention and efforts of researchers over the years. In the past 20 years, the studies in this scenario distinguished primarily by the nature of the coupling and the type or strength of damping. Particularly, under the premise that the Timoshenko beam model is a...

In this article, we consider a linear Timoshenko system with a strong damping and a strong constant delay acting on the transverse displacement of the beam. Using the semigroup techniques, we first establish the global well‐posedness result under a condition on the weight of the delayed feedback and the weight of the nondelayed feedback. Then, we s...

The paper is concerned with a porous elastic problem in a past history framework. We study its long-time behavior through the corresponding autonomous dynamical system. Instead of showing the directly the system has a bounded absorbing set, we show the system is gradient system and asymptotic smoothness, and prove the existence of a global attracto...

DESCRIPTION Over the last thirty years the theory of generalized special functions has proved its importance in a variety of fields from theoretical to practical issues in biosciences and engineering. It has been developed for decades as a generalization of the special function theory in the complex plane to higher dimensions and also considered as...

In this paper, we investigate the decay properties of suspension bridge with memories in one dimension. To prove our results, we use the energy method to build some very delicate Lyapunov functionals that give the desired results.

In this paper, a three-layer Rao-Nakra sandwich beam is considered where the core viscoelastic layer is constrained by the purely elastic or smart piezoelectric outer layers. In the model, uniform bending motions of the overall laminate are coupled to the longitudinal motions of the outer layers. Together with nonlinear damping and source terms, th...

In this paper, we consider a Timoshenko type system coupled with parabolic equation that represents the thermal effect given by the Gurtin-Pipkin law while taking into account that the temperature influences on the shear force. We establish the global existence of solution the behavior of the solution. We also prove the lack of the exponential stab...

In this paper, we study the well-posedness and asymptotic stability to a thermoelastic laminated beam with nonlinear weights and time-varying delay. To the best of our knowledge, there are no results on the system and related Timoshenko systems with nonlinear weights. On suitable premises about the time delay and the hypothesis of equal-speed wave...

In this paper we are concerned with a one-dimensional linear theory of inho-mogeneous porous-thermo-elastic materials with microtemperatures. The main results contain the global well-posedness and stability of the system. By using Lumer-Philips theorem, we prove that the system is well posed. By using energy method, we establish exponential decay r...

In this work, we prove a general and optimal decay estimates for the solution energy of a new thermoelastic Timoshenko system with viscoelastic law acting on the transverse displacement. Therefore, exponential and polynomial decay rates are obtained as particular cases. The result is obtained under the assumption of equal speed of wave propagation.

This is a complementation work of the paper referred in Jorge Silva, Muñoz Rivera and Racke (Appl Math Optim 73:165–194, 2016) where the authors proposed a semi-linear viscoelastic Kirchhoff plate model. While in [28] it is presented a study on well-posedness and energy decay rates in a historyless memory context, here our main goal is to consider...

In this paper, we consider the asymptotic behavior of solutions for the transmission problem for Timoshenko beam with memory. We show that the stability of the system holds for a much larger class of relaxation functions and get better decay rate than the ones existing in the literature. Our method of proof is based on the multipliers techniques an...

In this paper, we investigate a suspension bridge equation with past history and time delay effects, defined in a bounded domain \Omega of RN. Many researchers have considered the well-posedness, energy decay of solution and existence of global attractors for suspension bridge equation without memory or delay. But as far as we know, there are no re...

This paper is concerned with the study on the existence of attrac-tors for a nonlinear porous elastic system subjected to a delay-type damping in the volume fraction equation. The study will be performed, from the point of view of quasi-stability for infinite dimensional dynamical systems and from then on we will have the result of the existence of...

In this paper, we consider a coupled Lamé system only with viscoealstic dampings. By assuming a more general of relaxation functions and by using some properties of convex functions, we establish optimal explicit and general energy decay results to the system. This result improves previous results in the literature.

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 syste...

In this paper, we are concerned with a coupled viscoelastic wave system with Balakrishnan‐Taylor dampings, dynamic boundary conditions, source terms, and past histories. Under suitable assumptions on relaxation functions and source terms, we prove the global existence of solutions by potential well theory and we establish a more general decay resul...

In this paper, we consider a laminated Timoshenko beam with boundary conditions of a memory type. This structure is given by two identical uniform layers, one on top of the other, taking into account that an adhesive of small thickness bonds the two surfaces and produces an interfacial slip. Under the assumptions of wider classes of kernel function...

In [6] Beniani, Taouaf and Benaissa studied a coupled viscoelastic Lamé system with strong dampings and established a general decay result. In this paper, we continue to study the system. Assuming gi0(t) ≤−ξi(t)Hi(gi(t)), i = 1,2, we establish an explicit and general decay result, which is optimal, to the system. This result improves earlier result...

This paper is concerned with a nonlinear viscoelastic Kirchhoff plate u t t t − σ Δ u t t t + Δ 2 u t − ∫ 0 t g t − s Δ 2 u s d s = div F ∇ u t . By assuming the minimal conditions on the relaxation function g : g ′ t ≤ ξ t G g t , where G is a convex function, we establish optimal explicit and general energy decay results to the system. Our result...

In this paper, we are concerned with a linear thermoelastic laminated Timoshenko beam, where the heat conduction is given by Cattaneo’s law. We firstly prove the global well posedness of the system. For stability results, we establish exponential and polynomial stabilities by introducing a stability number . 1. Introduction In this paper, we addre...

In this paper, we consider the nonlinearly damped nonlinear coupled wave and Petrovsky system $$\begin{aligned}&u'' + \Delta ^{2} u+ av + g_{1}(u')=f_{1}(u,v), \\&v'' - \Delta v+ au + g_{2}(v')=f_{2}(u,v). \end{aligned}$$We prove the global existence of solutions by means of the stable set method in \(H_{0}^{2}(\Omega )\times H^1_0(\Omega )\) combi...

This paper concerns a nonlinear viscoelastic wave equation with time-dependent delay. Under suitable assumption of a relation between the weight of the delay and the weight of the term without delay, we firstly prove the global existence of weak solutions by the combination of the Galerkin method and potential well theory. In addition, by assuming...

In this paper, we study the asymptotic behavior for a Bresse-Timoshenko type system with time-dependent delay terms. Our results follow a recent approach given by Almeida Júnior and Ramos (Zeitschrift für angewandte Mathematik und Physik. 68, 1-31. 2017) where they showed that the viscous damping acting on angle rotation of the classical Bresse-Tim...

This paper studies a porous elasticity system with past history. By introducing a new variable, we establish an explicit and a general decay of energy for the case of equal-speed wave propagation as well as for the nonequal-speed case. To establish our results, we mainly adopt the method developed by Guesmia, Messaoudi and Soufyane [Electron. J. Di...

We consider a one-dimensional continuous thermal model of nuclear matter, which is described by a compressible Navier-Stokes-Poission system with a non-monotone equation of state owing to the effective Skyrme nuclear interaction between particles. We prove the global existence of solutions in H4 space for a free boundary value problem with a possib...

In this paper we are concerned with a viscoelastic wave equation with Balakrishnan-Taylor damping and frictional damping. By using the multiplier method and some properties of convex functions, we establish general energy decay rates of the equation without imposing any growth assumption near the origin on the frictional term and strongly weakening...

The paper considers a one-dimensional linear porous system with finite memory effective on the equilibrated stress vector. By assuming minimal conditions on the relaxation function, we establish an optimal explicit and energy decay rate for which exponential and polynomial rates are special cases. This result is new and substantially improves earli...

We consider in this article a one spatial variable transmission problem in mixed type I and type II thermoelastic system with infinite memory acting in the second part. The main contributions are to show that the infinite memory lets our problem dissipative and that the t^{-1} is the sharp decay rate. That is to show that for this types of material...

Two classes of plate equations with past history and strong time-dependent delay in the internal feedback are considered. Our results contain the global well-posedness and exponential stability of the two systems. We prove the global well-posedness of a system with rotational inertia without any restrictions on $\mu_1,\mu_2$, and the system without...

This paper is concerned with pullback dynamics of a 3D Navier-Stokes equations with variable viscosity and subject to perturbations of time-dependent external forces. Under suitable assumptions on the external force, which is possibly unbounded, we establish the existence of finite-dimensional minimal pullback attractor in a general setting involvi...

In this paper, we study a viscoelastic wave equation with dynamic boundary conditions, source term and a nonlinear weak damping localized on a part of the boundary and past history. Under suitable assumptions, we establish an explicit and general decay result of energy by introducing suitable energy and perturbed Lyapunov functionals and some prope...

This article focuses on the optimal regularity and long-time dynamics of solutions of a Navier-Stoke-Voigt equation with non-autonomous body forces in non-smooth domains. Optimal regularity is considered, since the regularity H10∩H2 cannot be achieved. Given the initial data in certain spaces, it can be shown that the problem generates a well-defin...

This paper concerns a $n$-dimensional spherically symmetric model for the combustion of a viscous, compressible, radiative-reactive gas with a chemical kinetics equation. Under suitable assumptions, we establish some uniform-in-time estimates of global solutions to this model which improve some known results.

In previous work, Apalara considered a one-dimensional porous elasticity system with memory and established a general decay of energy for the system in the case of equal-speed wave propagations. In this paper, we extend the result to the case of non-equal wave speeds, which is more realistic from the physics point of view.

An extensible viscoelastic plate equation with a nonlinear time-varying delay feedback and nonlinear source term is considered. Under suitable assumptions on relaxation function, nonlinear internal delay feedback and source term, we establish general decay of energy by using the multiplier method if the weight of weak dissipation and the delay sati...

A plate equation with past history and time-varying delay in the internal feedback is considered. The main result is the long-time dynamics of the system. Under suitable assumptions on real numbers μ1 and μ2,we establish the quasi-stability property of the system and obtain the existence of a global attractor which has finite fractal dimension. We...

This paper is concerned with laminated beams modeled from the well established Timoshenko system with time delays and boundary feedbacks. By using semi-group method, we prove the global well-posedness of solutions. Assuming the weights of the delay are small, we establish the exponential decay of energy to the system by using an appropriate Lyapuno...

In this paper, we prove the large-time behavior, as time tends to infinity, of solutions in Hi×H0i×Hi+1(i=1,2) and H4×H04×H4 for a system modeling the nematic liquid crystal flow, which consists of a subsystem of the compressible Navier-Stokes equations coupling with a subsystem including a heat flow equation for harmonic maps.

A linear viscoelastic wave equation with density and time delay in the whole space Rⁿ (n ≥ 3) is considered. In order to overcome the difficulties in the non-compactness of some operators, we introduce some weighted spaces. Under suitable assumptions on the relaxation function, we establish a general decay result of solution for the initial value p...

A semilinear Timoshenko-Coleman-Gurtin system is studied. The system describes a Timoshenko beam coupled with a temperature with Coleman-Gurtin law. Under some assumptions on nonlinear damping terms and nonlinear source terms, we establish the global well-posedness of the system. The main result is the long-time dynamics of the system. By using the...

A viscoelastic wave equation with strong damping and strong time-dependent delay in the internal feedback is considered. Under the assumption |μ2|<1−dμ1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidem...

This paper is concerned with a class of plate equation with past history and time-varying delay in the internal feedback $$\begin{aligned} u_{tt}+\alpha \Delta ^2 u-\int \limits ^t_{-\infty }g(t-s)\Delta ^2 u(s)\mathrm{d}s+\mu _1u_t+\mu _2u_t(t-\tau (t))+f(u)=h(x), \end{aligned}$$defined in a bounded domain of \({\mathbb {R}}^n\)\((n\ge 1)\) with s...

In this paper, we study the long-time dynamics of solutions to a nonlinear nonautonomous extensible plate equation with a strong damping. Under some suitable assumptions on the initial data, the nonlinear term and external force, we establish the existence of global solutions that generate a family of processes for the problem and obtain uniform at...

In this paper, we consider a one-dimensional porous thermoelasticity system with past history, which contains a porous elasticity in the presence of a visco-porous dissipation, a macrotemperature effect and temperature difference. We establish the exponential stability of the system if and only if the equations have the same wave speeds, and obtain...

This paper is concerned with a nonlinear Timoshenko system with a time delay term in the internal feedback together with initial data and Dirichet boundary conditions. Under some suitable assumptions on the weights of feedback, we obtain the existence of a global attractor with finite fractal dimension for the case of equal speed wave propagation....

In this paper we study the long-time dynamics of the semilinear viscoelastic equation utt−Δutt−Δu+∫0∞μ(s)Δu(t−s)ds+f(u)=h,(Formula presented.) defined in a bounded domain of (Formula presented.) with Dirichlet boundary condition. The functions (Formula presented.) and (Formula presented.) represent forcing terms and the kernel function (Formula pre...

This paper is concerned with a nonlinear Timoshenko system modeling clamped thin elastic beams with time delay. The delay is defined on a feedback term associated to the equation for rotation angle. Under suitable assumptions on the data, we establish the well-posedness of the problem with respect to weak solutions. We also establish the exponentia...

A plate equation with a memory term and a time delay term in the internal feedback is investigated. 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. Moreover, by using energy perturbation method, we prove a general decay...

In this paper, assuming suitable hypotheses on the transport coefficients, we prove the large-time behavior, as time tends to infinity, of solutions in H2H2 and H3H3 (see below for their definitions) for the one-dimensional viscous heat-conducting gas with radiation.

In this paper, we consider the initial-boundary value problems for the 1D thermodiffusion equations in a bounded region. Using the semigroup approaches and the multiplier methods, we obtain the global existence and asymptotic behavior of solutions for homogeneous, nonhomogeneous and semilinear thermodiffusion equations subject to various boundary c...

In this paper, we study the global existence of solutions for the compressible Navier-Stokes equations with a non-autonomous external force and a heat source in H4. Under suitable assumptions, we obtain the large-time behaviour of solutions in H4.

In this paper, we are concerned with a system of nonlinear viscoelastic wave equations with initial and Dirichlet boundary conditions in ( ). Under suitable assumptions, we establish a general decay result by multiplier techniques, which extends some existing results for a single equation to the case of a coupled system. MSC: 35L05, 35L55, 35L...

In this paper, assuming suitable hypotheses on the transport coefficients, we prove the large-time behavior, as time tends to infinity, of solutions in Hi=Hi×H0i×Hi×Hi+1 (i=1,2i=1,2) for the one-dimensional infrarelativistic model of a compressible viscous gas with radiation.