Random attractor for stochastic non-autonomous damped wave equation with critical exponent
Random attractor for stochastic non-autonomous damped wave equation with critical exponent
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DOI：
10.3934/dcds.2017022
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发表时间：
2016-11
影响因子：
1.1
通讯作者：
Zhaojuan Wang;Shengfan Zhou
中科院分区：
文献类型：
--
作者：
Zhaojuan Wang;Shengfan Zhou
本文证明了具有临界指数和加性白噪声的随机非自治阻尼波动方程的随机吸引子的存在性，并得到了随机吸引子分形维数的上界。首先，通过仔细分割第一阶随机演化方程中线性算子的正性，并通过两种不同的模态仔细分解系统的解，证明了随机吸引子的存在性，然后用递推方法证明了随机吸引子在高正则空间中的有界性。在此基础上，建立了循环随机不变集分形维数的定界准则，并应用该准则求出了所考虑系统随机吸引子的分形维数的上界。
In this paper, we prove the existence of random attractor and obtainan upper bound of fractal dimension of random attractor forstochastic non-autonomous damped wave equation with criticalexponent and additive white noise. We first prove the existence of arandom attractor by carefully splitting the positivity of the linearoperator in the corresponding random evolution equation of the firstorder in time and by carefully decomposing the solutions of systemthrough two different modes, and we show the boundedness of randomattractor in a higher regular space by a recurrence method. Then weestablish a criterion to bound the fractal dimension of a randominvariant set for a cocycle and applied these conditions to get anupper bound of fractal dimension of the random attractor ofconsidered system.