scholarly journals Exponential stability of mild solutions of stochastic partial differential equations with delays

1999 ◽  
Vol 17 (5) ◽  
pp. 743-763 ◽  
Author(s):  
Tomás Caraballo ◽  
Kai Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Stability ◽  
Stochastic Partial Differential Equations ◽  
Mild Solutions ◽  
Partial Differential

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.

scholarly journals On the Convergence of Solutions for SPDEs under Perturbation of the Domain

2016 ◽  
Vol 2016 ◽  
pp. 1-7
Author(s):  
Zhongkai Guo ◽  
Jicheng Liu ◽  
Wenya Wang
Keyword(s):  
Boundary Condition ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Dirichlet Boundary Condition ◽  
Stochastic Partial Differential Equations ◽  
Dirichlet Boundary ◽  
Mild Solutions ◽  
Partial Differential ◽  
Domain Perturbation ◽  
Convergence Of Solutions

We investigate the effect of domain perturbation on the behavior of mild solutions for a class of semilinear stochastic partial differential equations subject to the Dirichlet boundary condition. Under some assumptions, we obtain an estimate for the mild solutions under changes of the domain.

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