Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delays

The aim of this paper is devoted to obtain some sufficient conditions for the exponential stability in  -moment as well as almost surely exponential stability for mild solution of neutral stochastic partial differential equations with delays by establishing an integral-inequality. Some well-known results are generalized and improved. Finally, an example is given to show the effectiveness of our results.

[1]  J. Zabczyk,et al.  Stochastic Equations in Infinite Dimensions , 2008 .

[2]  T. E. Govindan,et al.  Stability of Mild Solutions of Stochastic Evolution Equations with Variable Delay , 2001 .

[3]  Li Wan,et al.  Exponential stability of non-autonomous stochastic partial differential equations with finite memory , 2007, 0710.2082.

[4]  Takeshi Taniguchi,et al.  Asymptotic stability theorems of semilinear stochastic evolution equations in hilbert spaces , 1995 .

[5]  EXPONENTIAL STABILITY FOR STOCHASTIC DIFFERENTIAL DELAY EQUATIONS IN HILBERT SPACES , 1991 .

[6]  Kai Liu,et al.  A note on almost sure exponential stability for stochastic partial functional differential equations , 2000 .

[7]  T. Taniguchi Almost sure exponential stability for stochastic partial functional differential equations , 1998 .

[8]  Amnon Pazy,et al.  Semigroups of Linear Operators and Applications to Partial Differential Equations , 1992, Applied Mathematical Sciences.

[9]  T. Caraballo Asymptotic exponential stability of stochastic partial differential equations with delay , 1990 .

[10]  Linear autonomous neutral differential equations in a Banach space , 1977 .

[11]  Kai Liu,et al.  Existence, Uniqueness, and Asymptotic Behavior of Mild Solutions to Stochastic Functional Differential Equations in Hilbert Spaces , 2002 .

[12]  Xuerong Mao,et al.  Exponential stability of non-linear stochastic evolution equations , 1998 .

[13]  T. Caraballo,et al.  Partial differential equations with delayed random perturbations: existence uniqueness and stability of solutions , 1993 .

[14]  A. Ichikawa Stability of semilinear stochastic evolution equations , 1982 .

[15]  Jiaowan Luo,et al.  Fixed points and exponential stability of mild solutions of stochastic partial differential equations with delays , 2008 .

[16]  Takeshi Taniguchi,et al.  The exponential stability for stochastic delay partial differential equations , 2007 .

[17]  刘 凯湘 Stability of infinite dimensional stochastic differential equations with applications , 2006 .

[18]  T. A. Burton,et al.  Stability by Fixed Point Theory for Functional Differential Equations , 2006 .

[19]  T. Govindan EXISTENCE AND STABILITY OF SOLUTIONS OF STOCHASTIC SEMILINEAR FUNCTIONAL DIFFERENTIAL EQUATIONS , 2002 .

[20]  Análisis Numérico,et al.  EXPONENTIAL STABILITY OF MILD SOLUTIONS OF STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS WITH DELAYS , 2001 .

[21]  Yi Shen,et al.  New criteria on exponential stability of neutral stochastic differential delay equations , 2006, Syst. Control. Lett..

[22]  Kai Liu,et al.  Razumikhin-Type Theorems of Infinite Dimensional Stochastic Functional Differential Equations , 2005, Systems, Control, Modeling and Optimization.

[23]  U. Haussmann Asymptotic stability of the linear ito equation in infinite dimensions , 1978 .

[24]  T. Caraballo,et al.  The exponential stability of neutral stochastic delay partial differential equations , 2007 .

[25]  N. Mahmudov Existence and Uniqueness Results for Neutral SDEs in Hilbert Spaces , 2006 .

[26]  Jiaowan Luo Fixed points and stability of neutral stochastic delay differential equations , 2007 .