推广的B-BBM方程的整体吸引子和指数吸引子

本文对耗散的推广的B－BBM方程的长时间动力学行为进行了研究，证明了该方程整体吸引子和指数吸引子的存在性。     

带时滞项的Boussinesq-Beam方程的吸引子

研究了带时滞项的Boussinesq-Beam方程的动力学行为,在耗散合适的条件下,证明了该边值问题具有拉回吸引子和一致正向吸引子.     

耗散KDV型方程Cauchy问题的整体吸引子

该文对耗散ＫＤＶ型方程的动力学行为进行了讨论,得到了该方程在Ｈ＾２（Ｒ＾１）上存在整体吸引子。     

非扰动耗散Hamiltonian振幅波方程的整体吸引子

本文研究了非扰动耗散Hamiltonian振幅波方程的长时间行为，通过算子分解和能量方程，我们分别得到了在E0和E1空间的整体吸引子。     

非自治Ginzburg-Landau方程的有限维行为

本文研究Ω R~n(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为。证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A_1。当外力是时间拟周期时,得到了吸引子A_1的Hausdorff维数的上界估计,当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L~2(Q)上存在唯一周期解,该周期解指数吸引H中的任何有界集。     

非自治Ginzburg-Landau方程的有限维行为

本文研究Ω(с)Rn(n=1,2,3)上具有几乎周期外力的非自治Ginzburg-Landau方程的有限维行为.证明了非自治Ginzburg-Landau系统存在紧的一致吸引子A1.当外力是时间拟周期时,得到了吸引子A1的Hausdorff维数的上界估计.当外力是时间周期时,证明了吸引子里一定含有周期解,而且当耗散系数λ满足适当条件时,系统在空间H=L2(Ω)上存在唯一周期解,该周期解指数吸引H中的任何有界集.     

耗散Camassa-Holm方程的吸引子

本文就一个新的色散水波方程Camassa-Hohn方程的动力学行为进行了研究，讨论了耗散CH方程的解的整体存在，获得了其解半群在H^2中全局吸引子的存在性．     

带弱耗散的两维非自治不可压Navier-Stokes方程的一致吸引子

研究了描述流体力学规律的一类带有弱耗散两维非自治不可压Navier-Stokes方程解的长时间行为.在给出自治外力项和初值的合理假设条件下,运用弱连续方法,可以得到系统一致吸引子的存在性.     

发展超导问题的局部耗散性和吸引子

本文得到了在Lorentz规范下一类发展超导问题解的整体存在性、局部耗散 性和吸引子的存在性.     

耗散Zakharov方程组柯西问题的指数吸引子

文［１］中证明了耗散Ｚａｋｈａｒｏｖ方程组的最大吸引子的存在性．该文采用算子分解技术和构造犎２×犎１×犔２（犚）中渐进紧不变集的方法,得到了一维无界区域上耗散Ｚａｋｈａｒｏｖ方程组柯西问题的指数吸引子．     

Reflection and Refraction of Solitons by the KdV–Burgers Equation in Nonhomogeneous Dissipative Media

We study the behavior of the soliton that encounters a barrier with dissipation while moving in a nondissipative medium. We use the Korteweg–de Vries–Burgers equation to model this situation. The modeling includes the case of a finite dissipative layer similar to a wave passing through air–glass–air and also a wave passing from a nondissipative layer into a dissipative layer (similar to light passing from air to water). The dissipation predictably reduces the soliton amplitude/velocity. Other effects also occur in the case of a finite barrier in the soliton path: after the wave leaves the dissipative barrier, it retains the soliton form, but a reflection wave arises as small and quasiharmonic oscillations (a breather). The breather propagates faster than the soliton passing through the barrier.     

单模光纤中光孤立子传播的长距离行为(英文)

研究描述单模光纤中光孤立子传播的具光纤损耗项的三阶非线性Ｓｃｈｒｏｄｉｎｇｅｒ方程,首先证明了整体解的存在唯一性结果,然后证明其长距离行为由紧的整体吸引子刻画,并给出了吸引子的Ｈａｕｓｄｏｒｆｆ维数和分形维数的上界估计,最后研究了吸引子的正则性．     

受迫耗散Boussinesq方程的可积性质和孤波解的探讨

考虑到耗散效应和地形外力,Rossby波的振幅可由受迫耗散Boussinesq方程来描述.当包含这两项时,模型比较复杂,不具有Painleve性质.通过将模型双线性化,双线性方法是一个可寻找孤波解和B(a|¨)cklund变换的方法.通过截断的Painleve展开式,得到了将方程双线性化的合适的因变量变换.然后得到了受迫耗散Boussinesq方程的单孤波解和B(a|¨)cklund变换.     

Hausdorff dimension of a random invariant set

The notion of random attractor for a dissipative stochastic dynamical system has recently been introduced. It generalizes the concept of global attractor in the deterministic theory. It has been shown that many stochastic dynamical systems associated to a dissipative partial differential equation perturbed by noise do possess a random attractor. In this paper, we prove that, as in the case of the deterministic attractor, the Hausdorff dimension of the random attractor can be estimated by using global Lyapunov exponents. The result is obtained under very natural assumptions. As an application, we consider a stochastic reaction-diffusion equation and show that its random attractor has finite Hausdorff dimension.     

APPROXIMATION TO THE GLOBAL ATTRACTOR FOR A NONLINEAR SCHRODINGER EQUATION

Abstract. In the present paper, we deal with the long-time behavior of dissipative partial differenttial equations, and we construct the approximate inertial mardfolds for the nonlbaear Stringer equation with a zero order dlssipation. The order of approximation of these manlfolde to the global attractor is derived.     

Attractors for partly dissipative lattice dynamic systems in weighted spaces

In this paper, we study the asymptotic behavior of solutions for the partly dissipative lattice dynamical systems in weighted spaces. We first establish the dynamic systems on infinite lattice, and then prove the existence of the global attractor in weighted spaces by the asymptotic compactness of the solutions. It is shown that the global attractors contain traveling waves. The upper semicontinuity of the global attractor is also considered by finite-dimensional approximations of attractors for the lattice systems.     

Asymptotic behavior of a class of stochastic nonlinear wave equations with dispersive and dissipative terms

This paper is concerned with the asymptotic behavior of solutions of a stochastic nonlinear wave equation with dispersive and dissipative terms defined on an unbounded domain. It is proved that the random dynamical system generated by the equation has a random attractor in a Sobolev space. To overcome the difficulty caused by the non-compactness of Sobolev embeddings on unbounded domains, a cut-off method and a decomposition trick are combined to prove the asymptotic compactness of the solutions.     

Regularity of the Attractor for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities

Abstract In the present paper, the existence of global attractor for dissipative Hamiltonian amplitude equationgoverning the modulated wave instabilities in E_0 is considered.By a decomposition of solution operator,it isshown that the global attractor in E_0 is actually equal to a global attractor in E_1.     

Large Time Behavior via the Method of ?-Trajectories

The method of ?-trajectories is presented in a general setting as an alternative approach to the study of the large-time behavior of nonlinear evolutionary systems. It can be successfully applied to the problems where solutions suffer from lack of regularity or when the leading elliptic operator is nonlinear. Here we concentrate on systems of a parabolic type and apply the method to an abstract nonlinear dissipative equation of the first order and to a class of equations pertinent to nonlinear fluid mechanics. In both cases we prove the existence of a finite-dimensional global attractor and the existence of an exponential attractor.