scholarly journals The Asymptotic Behavior for Second-Order Neutral Stochastic Partial Differential Equations with Infinite Delay

2011 ◽  
Vol 2011 ◽  
pp. 1-15 ◽  
Author(s):  
Huabin Chen
Keyword(s):  
Asymptotic Behavior ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Stability ◽  
Mild Solution ◽  
Stochastic Partial Differential Equations ◽  
Infinite Delay ◽  
Second Order ◽  
Asymptotical Stability ◽  
Partial Differential

By establishing two Lemmas, the exponential stability and the asymptotical stability for mild solution to the second-order neutral stochastic partial differential equations with infinite delay are obtained, respectively. Our results can generalize and improve some existing ones. Finally, an illustrative example is given to show the effectiveness of the obtained results.

scholarly journals Exponential stability for neutral stochastic partial integro-differential equations of second order with poisson jumps

Filomat ◽  
2018 ◽  
Vol 32 (15) ◽  
pp. 5173-5190
Author(s):  
Alka Chadha
Keyword(s):  
Differential Equations ◽  
Exponential Stability ◽  
Mild Solution ◽  
Stochastic Partial Differential Equations ◽  
Existence And Uniqueness ◽  
Infinite Delay ◽  
Second Order ◽  
Poisson Jumps ◽  
Fixed Point Principle ◽  
Poisson Jump

This paper studies the existence, uniqueness and the exponential stability in p-th moment of the mild solution of neutral second order stochastic partial differential equations with infinite delay and Poisson jumps. The existence and uniqueness of the mild solution of neutral second order stochastic differential equation is first established by means of Banach fixed point principle and stochastic analysis. The exponential stability in the p-th moment for the mild solution to impulsive neutral stochastic integrodifferential equations with Poisson jump is obtained by establishing an integral inequality.

scholarly journals On stabilization of partial differential equations by noise

2001 ◽  
Vol 161 ◽  
pp. 155-170 ◽  
Author(s):  
Tomás Caraballo ◽  
Kai Liu ◽  
Xuerong Mao
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Partial Differential Equations ◽  
Finite Dimension ◽  
Infinite Dimension ◽  
Stability Criteria ◽  
Partial Differential ◽  
Almost Sure Exponential Stability

Some results on stabilization of (deterministic and stochastic) partial differential equations are established. In particular, some stability criteria from Chow [4] and Haussmann [6] are improved and subsequently applied to certain situations, on which the original criteria commonly do not work, to ensure almost sure exponential stability. This paper also extends to infinite dimension some results due to Mao [9] on stabilization of differential equations in finite dimension.

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