Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
Exponentially Stable Stationary Solutions for Stochastic Evolution Equations and Their Perturbation
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DOI：
10.1007/s00245-004-0802-1
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发表时间：
2004-08
影响因子：
1.8
通讯作者：
T. Caraballo;P. Kloeden;B. Schmalfuß
中科院分区：
文献类型：
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作者：
T. Caraballo;P. Kloeden;B. Schmalfuß
研究了一类具有Lipschitz连续非线性项的随机发展方程的指数稳定性。我们证明了一个非平凡的平稳解的存在性，这是指数稳定的，其中的平稳解是由随机变量的组合和维纳移位。我们还构造了具有较强的一致吸引有界集性质的平稳解。这些定态解的存在性来自随机动力系统及其吸引子的理论。此外，我们证明了一些扰动结果和制定条件的存在性平稳解的半线性随机偏微分方程Lipschitz连续非线性。
We consider the exponential stability of stochastic evolution equations with Lipschitz continuous non-linearities when zero is not a solution for these equations. We prove the existence of a non-trivial stationary solution which is exponentially stable, where the stationary solution is generated by the composition of a random variable and the Wiener shift. We also construct stationary solutions with the stronger property of attracting bounded sets uniformly. The existence of these stationary solutions follows from the theory of random dynamical systems and their attractors. In addition, we prove some perturbation results and formulate conditions for the existence of stationary solutions for semilinear stochastic partial differential equations with Lipschitz continuous non-linearities.