Global attractor for the Ginzburg-Landau thermoviscoelastic systems with hinged boundary conditions

This paper is concerned with the following one-dimensional nonlinear system of equations:

(0.1)     

Global attractor for a class of nonlinear lattices

We consider a class of nonlinear lattices with nonlinear damping

(0.1)     

GLOBAL PERIODIC ATTRACTOR OF ATHIRD-ORDER PHASE-LOCKED LOOP

1.IntroductionandPreliminariesInthispaper,weconsidertheequation-..rx 7isecZx ac(a Zitgx)isecZx 7btgx~Bsinat,(1.1)wherea>0,b>0,ac>0,0andu>0areconstats.Theequivalelltthirdordersystemis(1'1)0=ohasbeenstudiedbyL.Wang,M.Q.WangandZ.Q.Luin[1];theirresultshowsthatthezerosolutionof(1.1)0=oisuniformlyasymptoticallystable.Inthispaperwewillprovetheexistenceofaglobalperiodicattractorfor(1.l)providedIIIissmallenough.Thephysicalimplicationofthisresulti.e.,theloopcanstayinlockinspiteofitisperturbed.The…     

Trajectory attractor and global attractor for a two-dimensional incompressible non-Newtonian fluid

The authors construct the trajectory attractor and global attractor for an autonomous two-dimensional non-Newtonian fluid.     

Global attractor for a density-dependent sensitivity chemotaxis model

In this paper, a chemotaxi model with reproduction term in a bounded domain Ω ⊂ Rⁿ is discussed. The existence of a global-in-time solution and a global attractor for this model are obtained.     

Global existence and asymptotic behaviour for a nonlocal phase-field model for non-isothermal phase transitions

In this paper a nonlocal phase-field model for non-isothermal phase transitions with a non-conserved order parameter is studied. The paper extends recent investigations to the non-isothermal situation, complementing results obtained by H. Gajewski for the non-isothermal case for conserved order parameters in phase separation phenomena. The resulting field equations studied in this paper form a system of integro-partial differential equations which are highly nonlinearly coupled. For this system, results concerning global existence, uniqueness and large-time asymptotic behaviour are derived. The main results are proved using techniques that have been recently developed by P. Krej?í and the authors for phase-field systems involving hysteresis operators.     

Global attractor for a nonlinear plate equation with supported boundary conditions

In this paper, we consider a two-dimensional nonlinear equation

(∗)     

The global attractor of the damped forced Ostrovsky equation

The existence of the global attractor of the damped forced Ostrovsky equation in is proved for the forces in . Moreover, the global attractor of the equation in is actually a compact set in .     

Global attractor for thermoelasticity in shape memory alloys without viscosity

We consider a nonlinear system of thermoelasticity in shape memory alloys without viscosity. The existence and uniqueness of strong and weak solutions and the existence of a compact global attractor in an appropriate space are proved. Copyright © 2015 John Wiley & Sons, Ltd.     

Global attractor for the Kirchhoff type equation with a strong dissipation

The paper studies the longtime behavior of the Kirchhoff type equation with a strong dissipation utt−M(‖∇u^‖2)Δu−Δut+h(ut)+g(u)=f(x). It proves that the related continuous semigroup S(t) possesses in the phase space with low regularity a global attractor which is connected. And an example is shown.     

与KdV及BO方程相关的一类方程之全局解<英>

本文中,对下述方程 u_t (u~h/h)_x _x(—_x~2)~qu=0的柯西问题解建立了全局存在及唯一性,其中h≥2为自然数并且q≥1/2为实数,另外,讨论了当|t|→ ∞时问题解的渐近性。     

Global attractor for a low order ODE model problem for transition to turbulence

Many researchers have studied simple low order ODE model problems for fluid flows in order to gain new insight into the dynamics of complex fluid flows. We investigate the existence of a global attractor for a low order ODE system that has served as a model problem for transition to turbulence in viscous incompressible fluid flows. The ODE system has a linear term and an energy‐conserving, non‐quadratic nonlinearity. Standard energy estimates show that solutions remain bounded and converge to a global attractor when the linear term is negative definite, that is, the linear term is energy decreasing; however, numerical results indicate the same result is true in some cases when the linear term does not satisfy this condition. We give a new condition guaranteeing solutions remain bounded and converge to a global attractor even when the linear term is not energy decreasing. We illustrate the new condition with examples. Copyright © 2016 John Wiley & Sons, Ltd.     

Global attractor and its dimension estimates for the generalized dissipative KdV equation onR

In this paper we prove the existence of global attractor for the generalized dissipative KdV equation onR, and give an upper bound for its hausdorff and fractal dimensions.     

Global attractor for the m-semiflow generated by a quasilinear degenerate parabolic equation

Using theory of global attractors for multi-valued semiflows, we prove the existence of a global attractor for the m-semiflow generated by a parabolic equation involving the nonlinear degenerate operator in a bounded domain.     

Exponential attractor and its fractal dimension for a second order lattice dynamical system

We construct an exponential attractor for a second order lattice dynamical system with nonlinear damping arising from spatial discretization of wave equations in Rk. And we obtain fractal dimension of the exponential attractor and its finite-dimensional approximation.     

带阻尼项的二维 Navier-Stokes 方程的 全局吸引子

考虑了带阻尼的二维Navier-Stokes方程在全空间中解的长时间行为,证明了相应的涡量方程存在(L~2(R~2),H~1(R~2))-吸引子.     

Global attractor for a nonlinear viscoelastic model

In this paper we establish the existence of global attractors of a semiflow and a semigroup for a nonlinear 1-d viscoelasticity in two frameworks. We exploit the properties of the analytic semigroup to show the compactness for the semiflow and semigroup generated by the weak global solutions.     

Global attractor for heat convection problem in a micropolar fluid

The article is devoted to describe asymptotics in the heat convection problem for a micropolar fluid in two dimensions. We show the existence and the uniqueness of global in time solutions and then prove the existence of a global attractor for considered model. Next, the Hausdorff dimension of the global attractor is estimated. Copyright © 2006 John Wiley & Sons, Ltd.     

Existence and regularity of the global attractor for a weakly damped forced shallow water equation in H

In this paper we prove the existence of the global attractor for a weakly damped forced shallow water equation in . Moreover, we show that the global attractor is actually compact in . The main method is the combination of the energy equation, a suitable splitting of the solutions, and bilinear estimates in Bourgain spaces.