具有线性乘积白噪声的随机非自治吊桥方程的随机指数吸引子

本文考虑具有线性乘积白噪声的随机非自治吊桥方程长时间行为.首先,建立了所研究共圈系统的适定性;第二步,研究了该系统随机吸引子的存在性;第三步,当随机系数趋于0时,得到了随机吸引子的上半连续性;第四步,通过``迭代''法证明了随机吸引子在高正则空间中的正则性;最后,给出了该系统随机指数吸引子的存在性,同时得到了吸引子的有限分形维数.

Random Exponential Attractor for Stochastic Non-autonomous Suspension Bridge Equation with Linear Multiplicative White Noise

In this paper, we mainly consider the long-time behavior of stochastic non-autonomous suspension bridge equation by linear multiplicative white noise with small coefficient. First step, the well-posedness for the cocycle associated with the considered system is established. Second step, the existence of random attractor for the system is investigated. Third step, the upper semicontinuity of random attractor is also provided when the coefficient of random term approaches zero. Fourth step, we prove the regularity of random attractor in a higher regular space by the ``iteration'' method. Finally, we give the existence of a random exponential attractor for the considered system, which implies the finiteness of fractal dimension of random attractor.