Bixiang Wang

Attractors for reaction-diffusion equations in unbounded domains

Abstract In this paper, we study the asymptotic behaviour of solutions for parabolic non-linear evolution equations in R n . We prove the asymptotic compactness of the solutions and then establish the existence of the global attractor in L 2 ( R n ) .

ATTRACTORS FOR LATTICE DYNAMICAL SYSTEMS

We study the asymptotic behavior of solutions for lattice dynamical systems. We first prove asymptotic compactness and then establish the existence of global attractors. The upper semicontinuity of the global attractor is also obtained when the lattice differential equations are approached by finite-dimensional systems.

Finite dimensional behaviour for the derivative Ginzburg-Landau equation in two spatial dimensions

Abstract In this paper, we study the long time behaviour of the solutions for the generalized derivative Ginzburg-Landau equation in two spatial dimensions. We show the existence of the global attractor for this equation and establish the estimates of the upper bounds of Hausdorff and fractal dimensions for the global attractor.

Poisson–Nernst–Planck Systems for Narrow Tubular-Like Membrane Channels

We study global asymptotic behavior of Poisson–Nernst–Planck (PNP) systems for flow of two ion species through a narrow tubular-like membrane channel. As the radius of the cross-section of the three-dimensional tubular-like membrane channel approaches zero, a one-dimensional limiting PNP system is derived. This one-dimensional limiting system differs from previously studied one-dimensional PNP systems in that it encodes the defining geometry of the three-dimensional membrane channel. To justify this limiting process, we show that the global attractors of the three-dimensional PNP systems are upper semi-continuous as the radius of the channel tends to zero.

Finite-dimensional behaviour for the Benjamin - Bona - Mahony equation

This paper deals with the asymptotic behaviour of solutions for the Benjamin - Bona - Mahony equation. We first show the existence of the global weak attractor for this equation in . And then by an idea of Ball, we prove that the global weak attractor is actually the global strong attractor. The finite-dimensionality of the global attractor is also established.

Existence and upper semicontinuity of attractors for stochastic equations with deterministic non-autonomous terms

We prove the existence and uniqueness of tempered random attractors for stochastic Reaction-Diffusion equations on unbounded domains with multiplicative noise and deterministic non-autonomous forcing. We establish the periodicity of the tempered attractors when the stochastic equations are forced by periodic functions. We further prove the upper semicontinuity of these attractors when the intensity of stochastic perturbations approaches zero.

Strong attractors for the Benjamin-Bona-Mahony equation

Abstract In this paper, we study the asymptotic behaviour of the solutions for the Benjamin-Bona-Mahony equation. We first present the existence of the global weak attractor in H per 2 for this equation. And then by an energy equation we show that the global weak attractor is actually the global strong attractor in H per 2 .

REGULARITY OF ATTRACTORS FOR THE BENJAMIN-BONA-MAHONY EQUATION

This paper deals with the regularity of the global attractor for the Benjamin-Bona-Mahony equation. We prove that the global attractor is smooth if the forcing term is smooth.

Existence of global attractors for the Benjamin–Bona–Mahony equation in unbounded domains

In this paper, we investigate the asymptotic behavior of the Benjamin–Bona–Mahony equation in unbounded domains. We prove the existence of a global attractor when the equation is defined in a three-dimensional channel. The asymptotic compactness of the solution operator is obtained by the uniform estimates on the tails of solutions.

Attractors for the Klein–Gordon–Schrödinger equation

In this paper we deal with the asymptotic behavior of solutions for the Klein–Gordon–Schrodinger equation. We prove the existence of compact global attractors for this model in the space Hl×Hl×Hl−1 for each integer l⩾1.