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Random attractors via pathwise mild solutions for stochastic parabolic evolution equations
Journal of Evolution Equations ( IF 1.4 ) Pub Date : 2021-04-12 , DOI: 10.1007/s00028-021-00699-x
Christian Kuehn , Alexandra Neamţu , Stefanie Sonner

We investigate the longtime behavior of stochastic partial differential equations (SPDEs) with differential operators that depend on time and the underlying probability space. In particular, we consider stochastic parabolic evolution problems in Banach spaces with additive noise and prove the existence of random exponential attractors. These are compact random sets of finite fractal dimension that contain the global random attractor and are attracting at an exponential rate. In order to apply the framework of random dynamical systems, we use the concept of pathwise mild solutions.



中文翻译:

随机吸引子通过随机抛物线演化方程的路径温和解

我们研究随机微分算子(SPDE)的长期行为,该微分算子取决于时间和潜在的概率空间。特别是,我们考虑了具有加性噪声的Banach空间中的随机抛物线演化问题,并证明了随机指数吸引子的存在。这些是具有有限分形维数的紧致随机集,其中包含全局随机吸引子,并且以指数速率吸引。为了应用随机动力系统的框架,我们使用了路径温和解的概念。

更新日期:2021-04-12
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