带可乘白噪声的非自治Schrödinger格点系统的随机指数吸引子

Random exponential attractor for non-autonomous Schrödinger lattice system with multiplicative white noise

主要研究带可乘白噪声的非自治随机Schrödinger格点系统,证明其存在随机指数吸引子.根据随机指数吸引子的存在性判据,首先,利用Ornstein-Uhlenbeck过程将系统转化成带随机参数而无白噪声的系统;其次,分解系统两解之差成2个部分,并估计某些随机变量的期望;最后,得到系统的随机指数吸引子的存在性.研究结果表明:所研究的系统的解的极限行为可用有限个参数来刻画.

It was mainly studied the existence of a random exponential attractor for non-autonomous Schrödinger lattice system with multiplicative white noise.According to the criteria of existence of a random exponential attractor,the objective stochastic system was transferred into a random system with random coefficients without noise through the Ornstein-Uhlenbeck process.Then it was decomposed the difference between two solutions into two parts,and estimated the expectations of some random variables.Finally,the existence of a random exponential attractor of the system was obtained.The results showed that the discussed limit behavior of the solution of the stochastic system coulde be characterized by finite parameters.