Persistent Homoclinic Orbits for Perturbed Nonlinear Schroding Equation With Derivative Term

In recent years there have been existence studies on the extensive of homoclinic orbits for mearly dissipative PDEs,which are chosely related to chaos.In this work,we consider the perturbe     

随机广义Ginzburg-Landau方程的吸引子

可以按轨道得到带白噪声的随机广义Ginzburg-Landau方程的唯一解并且能够验证该解可以产生随机系统, 从而证明了该随机系统在H¹₀中存在整体随机吸引子.     

广义Kuramoto-Sivashinsky型方程初值问题光滑整体解的存在性与破裂性

本文用积分估计和不动点原理证明了一类广义Kuramoto-Sivashinsky型方程初值问题光滑整体解的存在唯一性,并在不同情况下讨论了解的破裂性,并给出了导致破裂性的充分条件.     

非线性Schrdinger方程(Ⅰ):Bose-Einstein凝聚和怪波现象

非线性Schr(o|¨)dinger方程是非线性科学领域的最基本的方程之一,本文综述该方程的两个有趣的现象:怪波和Bose-Einstein凝聚,最后提出一些相关的公开问题.     

ILL-POSEDNESS FOR THE NONLINEAR DAVEY-STEWARTSON EQUATION

The nonlinear D-S equations on R^d, with general power nonlinearity and with both the focusing and defocusing signs, are proved to be ill-posed in the Sobolev space H^s whenever the exponent s is lower than that predicted by scaling or Galilean invariance, or when the regularity is too low to support distributional solutions. Authors analyze a class of solutions for which the zero-dispersion limit provides good approximations.     

一类广义Boussinesq型方程的Cauchy问题

证明了一类广义Boussinesq型方程Cauchy问题整体解的存在性与唯一性,并给出解在有限时刻爆破的充分条件.     

扰动非线性Schroedinger方程组的动力性态

研究具周期边界条件的扰动非线性Schroedinger方程组的动力性态，首先，在常值平面上用线性算子的谱对扰动和未扰动系统进行动力性态分析，然后利用奇异扰动理论和不动点原理证明局部不变流形的存在性．     

Existence and Upper Semicontinuity of.the Attractor for a Singularly PerturbedNavier-Stokes Equation

Suppose Rn, n = 2, 3 be a smooth bounded domain, we consider the perturbed NavierStokes equationThe study of this equation for ε= 0 has a long and rich history. In the two-dimensional case,the study is very successful and it is well known that the solutions of the equation define aC0-semigroup {S(t): t ≥ 0} in the space H = PL2 (where P is the projection onto thespace of divergence-free vector fields) and which has a global attractor Ac on H (see [1]). But,in the three-dimensional case, …