Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays

被引：112

作者：

Luo, Jiaowan ^{[1
]}

机构：

[1] Guangzhou Univ, Sch Math & Informat Sci, Dept Probabil & Stat, Guangzhou 510405, Guangdong, Peoples R China

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2008年 / 342卷 / 02期

基金：

中国国家自然科学基金;

关键词：

mild solution; stochastic delay partial differential equation; exponential stability;

D O I：

10.1016/j.jmaa.2007.11.019

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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.

引用

页码：753 / 760

页数：8

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