Global Existence, Asymptotic Behavior and Uniform Attractors for Damped Timoshenko Systems

In this paper, we consider the Timoshenko system as an initial-boundary value problem in a one-dimensional bounded domain. And then we establish the global existence and asymptotic behavior of solution by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor by using the method of uniform contractive function. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimate as that for establishing absorbing sets.

Global Existence, Asympotic Behavior and Uniform Attractors for Thermoelastic Systems

In this paper, we first establish the global existence and asymptotic behavior of solutions by multiplicative techniques, then further prove the existence of a uniform attractor for a thermoelastic system by using the method of uniform contractive functions. We finally investigate an alternative result of solutions for the semilinear thermoelastic systems by virtue of the semigroup method.

Global Existence,Asymptotic Behavior and Uniform Attractors of Timoshenko Systems with Gurtin-Pipkin Thermal Law

In this paper,we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques,then further prove the existence of a uniform attractor for Timoshenko systems with Gurtin-Pipkin thermal law by using the method of uniform contractive functions.The main advantages of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets.Moreover,we also investigate an alternative result of solutions to the semilinear Timoshenko systems by virtue of the semigroup method.

Global Existence,Asymptotic Behavior and Uniform Attractors for a Third Order in Time Dynamics

In this paper, a third order（in time） partial differential equation in R^n is con-sidered. By using semigroup method and constructing Lyapunov function, we establish the global existence, asymptotic behavior and uniform attractors in nonhomogeneous case. In addition, we also obtain the results of well-uosedness in semilinear case.

Uniform attractors for non-autonomous Klein-Gordon-Schrdinger lattice systems

The existence of a compact uniform attractor for a family of processes corre- sponding to the dissipative non-autonomous Klein-Gordon-SchrSdinger lattice dynamical system is proved. An upper bound of the Kolmogorov entropy of the compact uniform attractor is obtained, and an upper semicontinuity of the compact uniform attractor is established.

Global Existence,Asymptotic Behavior and Uniform Attractors for Non-autonomous Thermoelastic Systems

In this paper, we first establish the global existence and asymptotic behavior of solutions by using the semigroup method and multiplicative techniques, then further prove the existence of a uniform attractor for a non-autonomous thermoelastic system by using the method of uniform contractive functions. The main advantage of this method is that we need only to verify compactness condition with the same type of energy estimates as that for establishing absorbing sets. Moreover, we also investigate an alternative result of solutions to the semilinear thermoelastic systems by virtue of the semigroup method.

Existence of the Uniform Attractors for the Nonautonomous Suspension Bridge Equations with Strong Damping

In this paper we show the existence of the uniform attractors for the family of processes corresponding to the suspension bridge equations in H02 × L2 by a new concept of Condition （C＊） and the enegy estimats methods.

Uniform Attractors for Non-autonomous Brinkman-Forchheimer Equations with Delay

In this paper, we prove the existence of a uniform attractor for non-autonomous Brinkman-Forchheimer equations with general delay and time-dependent external force.

UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES

This paper is joint with [27]. The authors prove in this article the existence and reveal its structure of uniform attractor for a two-dimensional nonautonomous incompressible non-Newtonian fluid with a new class of external forces.

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

This paper studies the trajectory asymptotic behavior of a non-autonomous in- compressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

ATTRACTORS OF NONAUTONOMOUS SCHR?DINGER EQUATIONS

The long-time behaviour of a two-dimensional nonautonomous nonlinear Schrodinger equation is considered. The existence! of uniform attractor is proved and the upper bound of the uniform attractor's Housdorff dimension is given.

Dimension of the Uniform Attractor for a Non-autonomous Semilinear Thermoelastic Problem

In this paper, we prove the existence of a uniform attractor for the process associated with a non-antonomous semilinear thermoelastic problem. And under the certain parameter, we obtain an upper bound for the Hausdorff dimension of the uniform attractor.

Attractors of Dissipative Soliton Equation

In the paper ,we study longtime dynamic behavior of dissipative soliton equation existence of attractor ,geometrical structure of attractor dynamic behavior under the parametric perturbation of dissipative soliton equation.estimate of fractal dimension of attractor.

Asymptotic Behavior for A Class of Non-autonomous Nonclassical Parabolic Equations with Delay on Unbounded Domain

In this article,we investigate the longtime behavior for the following nonautonomous nonclassical parabolic equations on unbounded domain ut−∆ut−∆u+λu=f(x,u(x,t−ρ(t)))+g(x,t).Under some suitable conditions on the delay term f and the non-autonomous forcing term g,we prove the existence of uniform attractors in Banach space CH1(RN)for the multivalued process generated by non-autonomous nonclassical parabolic equations with delays in unbounded domain.

Uniform Compact Attractors for a Nonlinear Non-Autonomous Equation of Viscoelasticity

In this paper we prove the regularity, exponential stability of global solutions and existence of uniform compact attractors of semiprocesses, generated by the global solutions, of a two-parameter family of operators for a nonlinear onedimensional non-autonomous equation of viscoelasticity. We employ the properties of the analytic semigroup to show the compactness for the semiprocess generated by the global solutions.

Uniform Exponential Attractors for Second Order Non-autonomous Lattice Dynamical Systems

In this paper, the existence of a uniform exponential attractor for a second order non-autonomous lattice dynamical system with quasiperiodic symbols acting on a closed bounded set is considered. Firstly, the existence and uniqueness of solutions for the considered systems which generate a family of continuous processes is shown, and the existence of a uniform bounded absorbing sets for the processes is proved. Secondly, a semigroup defined on a extended space is introduced, and the Lipschitz continuity, a-contraction and squeezing property of this semigroup are proved. Finally, the existence of a uniform exponential attractor for the family of processes associated with the studied lattice dynamical systems is obtained.

LARGE TIME BEHAVIOR OF A THIRD GRADE FLUID SYSTEM

We consider the large time behavior of a non-autonomous third grade fluid sys- tem, which could be viewed as a perturbation of the classical Navier-Stokes system. Under proper assumptions, we firstly prove that the family of processes generated by the problem ad- mits a uniform attractor in the natural phase space. Then we prove the upper-semicontinuity of the uniform attractor when the perturbation tends to zero.

Uniform Exponential Attractor for Nonautonomous Partly Dissipative Lattice Dynamical System

In this paper,we consider the existence of a uniform exponential attractor for the nonautonomous partly dissipative lattice dynamical system with quasiperiodic external forces.

THE LONG TIME BEHAVIORS OF NON-AUTONOMOUS EVOLUTION SYSTEM DESCRIBING GEOPHYSICAL FLOW WITHIN THE EARTH

In this paper,the long time behaviors of non-autonomous evolution system describing geophysical flow within the earth are studied.The uniqueness and existence of the solution to the evolution system and the existence of uniform attractor are proven.Moreover,the upper bounds of the uniform attractor's hausdorff and Fractal dimensions are obtained.