LONG TIME BEHAVIOR FOR SOLUTION OF INITIAL BOUNDARY VALUE PROBLEM OF ONE CLASS OF SYSTEMS WITH MULTIDIMENSIONAL INHOMOGENEOUS GBBM EQUATIONS

The following initial-boundary value problem for the systems with multidimensional inhomogeneous generalized Benjamin-Bona-Mahony ( GBBM ) equations is reviewed. The existence of global attractors of this problem was proved by means of a uniform priori estimate for time.     

离散扰动NLS方程组的Smale马蹄与混沌(Ⅰ)——Poincaré映射

利用n维Conley-Moser条件证明了一类离散扰动非线性Schrdinger方程(NLS)的Smale马蹄的存在性．由以上结果,我们得到离散扰动NLS方程组存在不变集Λ,其动力系统与四符号变换拓扑共轭．     

一类多维非齐次GBBM方程初边值问题解的长时间行为

研究一类多维非齐次广义Benjamin-Bona-Mahony(GBBM)方程的初值边界问题,利用Sobolev插值不等式,做关于时间的一致性先验估计,证明该问题的整体吸引子的存在性．     

带有阻尼项的广义对称正则长波方程的指数吸引子

考虑了带有阻尼项的广义对称正则长波方程的整体快变动力学．证明了与该方程有关的非线性半群的挤压性质和指数吸引子的存在性．对指数吸引子的分形维数的上界也进行了估计．     

Ginzburg-Landau方程的非齐次初边值问题

研究具非线性边界条件的一类广义Ginzburg-Landau方程解的整体存在性．推导了Ginzburg-Landau方程的非齐次初边值问题光滑解的几个积分恒等式,由此得到了解的法向导数在边界上的平方模以及解的平方模和导数的平方模估计;通过逼近技巧、先验估计和取极限方法证明了Ginzburg-Landau方程的非齐次初边值问题整体弱解的存在性．     

Exact Blow—up Solutions for Multidimensional Landau—Lifshitz Equations

We present exact blow-up solutions for multidimensionalLandau--Lifshitz equations. It is shown that for any prescribed blow-up timethere are exact C∞--solutions which are blow-up at the blow-up timeand that the solutions are smooth except at theblow-up time.     

Exact Blow-up Solutions forMultidimensional Landau--Lifshitz Equations

We present exact blow-up solutions for multidimensional Landau-Lifshitz equations. It isshown that for any prescribed blow-up time there are exact C-solutions which are blow-up atthe blow-up time and that the solutions are smooth except at the blow-up time.In 1986, Zhou and Guo in [3] proved the global existence of weak solution for generalizedLandau-Lifshitz equations without Gilbert term in multidimensions. They consider the homogeneous boundary problemwith the initial value conditionfor …     

GLOBAL ATTRACTOR AND ITS DIMENSION ESTIMATES FOR THE GENERALIZED DISSIPATIVE KdV EQUATION ON R

1.IntroductionIn[41,GhidagliaprovedthatforthedissipativeKdVequation:withperiodicboundaryconditionu(x,t)=u(x L,t),thereexistsaweakglobalattractoroffinitedimension.Recently,[7]obtainedasimilarresultfortheperiodicboundaryproblemwhereor>0,g/0,7>0,fEC'(R),If15A]ul'--',6>0,Gi(0,0)=0,i=1,2andforevery(CI,'2)eR',However,feweffortsaredevotedtotheexistenceofglobalattractorinunboundeddomain.Themaindifficultinthiscaseliesinthatthelinearprincipleoperatorisnothavecompactresolventoperatorandthuswecannot…     

多变量铁磁链组齐次边值问题的弱解

本文对于多变量铁磁链方程组的齐次边值问题采用Galerkin方法证明了该问题弱解的存在性,并讨论了该问题的解当t→∞时的渐近性质和“blow up”问题。