ATTRACTORS FOR THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

By the interpolating inequality and a priori estimates in the weighted space,the existence of the global solutions for the Ginzburg-Landau equation coupled with the BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.

ATTRACTORS FOR GENERALIZED GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

By the interpolation inequality and a priori estimates in the weighted space, the existence of global solutions for generalized Ginzburg-Landau equation coupled with BBM equation in an unbounded domain is considered, and the existence of the maximal attractor is obtained.

EXPONENTIAL ATTRACTORS OF THE GINZBURG-LANDAU-BBM EQUATIONS IN AN UNBOUNDED DOMAIN

In this paper, the existence of the exponential attractors for the Ginzburg-Landau-BBM equations in an unbounded domain is proved by using weighted function and squeezing property.

Long-term Analysis of Degenerate Parabolic Equations in R^N

Longtime behavior of degenerate equations with the nonlinearity of polynomial growth of arbitrary order on the whole space RN is considered. By using-tra jectories methods, we proved that weak solutions generated by degenerate equations possess an（LU^2（R^N）, Lloc^2（R^N））-global attractor.Moreover, the upper bounds of the Kolmogorov ε-entropy for such global attractor are also obtained.

高维高阶非线性抛物方程整体解的存在性

在三维空间中考虑带高阶非线性项的复Ginzburg-Landau方程,通过引入权空间,应用内插不等式和先验估计,获得复Ginzburg-Landau方程整体解的存在性,更进一步,使用在权空间算子分解的方法,通过构造紧的正向不变吸收集,建立了整体强吸引子的存在性。

复Ginzburg-Landau方程在权空间上的长时间行为

在整体解的存在性的基础上,考虑带高阶非线性项的复Ginzburg-Landau方程的解的长时间行为。通过引入权空间,应用内插不等式和先验估计,获得复Ginzburg-Landau方程整体弱吸引子的存在性。进一步使用在权空间算子分解的方法,通过构造紧的正向不变吸收集,建立了整体强吸引子的存在性。

无界域上p-Laplacian方程在依赖参数的空间中动力学行为

研究无界域上非自治p-Laplacian系统u_t-div(ε(t)|▽u|^(p-2)▽u)+f(x,u)=g(x)的长时间动力学行为。在带参变量t的赋范空间中,建立方程所对应过程在拉回意义下吸收集的存在性。在无界区域上研究方程所对应的无穷维动力系统,最大的困难在于Sobolev嵌入缺乏紧性。为克服Sobolev嵌入缺乏紧性,利用一致"tail"估计,证明系统所对应的过程是渐近紧的,从而得到依赖于时间t的全局吸引子的存在性。

非自治耗散型Schrodinger方程在R^3的整体吸引子

研究R^3中无界域上非自治耗散型Schrodinger方程,首先得到整体解的存在唯一性结果,然后在 加权Sobolev空间用半群分解,能量方法和弱收敛方法,克服古典Sobolev嵌入的非紧性,证明方程在R3上存在 整体吸引子.

随机半线性强衰减波动方程在局部一致空间上的吸引子

在无界区域R^n中考虑了具有可加噪声的随机强衰减半线性波动方程的Cauchy问题,在相空间X=W_(lu)^(2,p)(R^n)×L_(lu)~p(R^n)中证明了该方程的整体可解性和随机吸引子的存在性.为解决该方程相关联的半群S(t,ω)的弱渐近紧性问题,首先证明了集合B_1∶=S(1,ω)γ^+(B_0)在空间D(L)=W_(lu)^(2,p)(R^n)×W_(lu)^(2,p)(R^n)中的有界性,其中B_0是半群S(t,ω)在相空间X中的吸收集;然后利用紧嵌入定理W_(lu)^(2,p)(R^n)×W_(lu)^(2,p)(R^n)■W_ρ^(1,p)(R^n)×W_ρ^(1,p)(R^n)得到了集合B_1在相空间X中的弱渐近紧性.