Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays
Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays
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DOI：
10.1016/j.jmaa.2007.11.019
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发表时间：
2008-06-15
影响因子：
1.3
通讯作者：
Luo, Jiaowan
中科院分区：
文献类型：
--
作者：
Luo, Jiaowan
首次利用不动点理论研究了随机时滞偏微分方程的稳定性。给出了温和解的p次平均指数稳定性和样本路径指数稳定性的条件。这些条件不要求时滞的单调递减行为，而这在[T.卡拉巴略湾Liu，随机时滞偏微分方程温和解的指数稳定性，Stoch。Anal. 17（1999）743-763; Ruhollan Jahanipur，Stability of stochastic delay evolution equations with monotone nonlinear，Stoch. Anal. 21（2003）161-181]。即使在这种特殊情况下，我们的结果也改进了[T.卡拉巴略湾Liu，随机时滞偏微分方程温和解的指数稳定性，Stoch。Anal. 17（1999）743-763]。(C)2007爱思唯尔公司All rights reserved.
The fixed-point theory is first used to consider the stability for stochastic partial differential equations with delays. Some conditions for the exponential stability in pth mean as well as in sample path of mild solutions are given. These conditions do not require the monotone decreasing behavior of the delays, which is necessary in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763; Ruhollan Jahanipur, Stability of stochastic delay evolution equations with monotone nonlinearity, Stoch. Anal. Appl. 21 (2003) 161-181]. Even in this special case, our results also improve the results in [T. Caraballo, K. Liu, Exponential stability of mild solutions of stochastic partial differential equations with delays, Stoch. Anal. Appl. 17 (1999) 743-763]. (C) 2007 Elsevier Inc. All rights reserved.