scholarly journals The exponential stability of neutral stochastic delay partial differential equations

2007 ◽  
Vol 18 (2/3, June) ◽  
pp. 295-313 ◽  
Author(s):  
T. Taniguchi ◽  
José Real ◽  
Tomás Caraballo
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exponential Stability ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

ON EXPONENTIAL STABILITY FOR STOCHASTIC DELAY PARTIAL DIFFERENTIAL EQUATIONS

2009 ◽  
Vol 09 (01) ◽  
pp. 121-134
Author(s):  
GUOSHENG YU ◽  
BING LIU
Keyword(s):  
Partial Differential Equations ◽  
Lyapunov Function ◽  
Differential Equations ◽  
Exponential Stability ◽  
Hilbert Spaces ◽  
Stability Criteria ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Finite Delay ◽  
Delay Partial Differential Equations

This paper is concerned with the exponential stability of energy solutions to a nonlinear stochastic delay partial differential equations with finite delay in separable Hilbert spaces. Some exponential stability criteria are obtained by constructing the Lyapunov function. As an application, one example is also given to illustrate our results.

scholarly journals The Existence, Uniqueness, and Controllability of Neutral Stochastic Delay Partial Differential Equations Driven by Standard Brownian Motion and Fractional Brownian Motion

2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Dehao Ruan ◽  
Jiaowan Luo
Keyword(s):  
Fixed Point ◽  
Brownian Motion ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Fractional Brownian Motion ◽  
Fixed Point Method ◽  
Standard Brownian Motion ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations

We focus on a class of neutral stochastic delay partial differential equations perturbed by a standard Brownian motion and a fractional Brownian motion. Under some suitable assumptions, the existence, uniqueness, and controllability results for these equations are investigated by means of the Banach fixed point method. Moreover, an example is presented to illustrate our main results.

Controllability for impulsive neutral stochastic delay partial differential equations driven by fBm and Lévy noise

2020 ◽  
Vol 21 (02) ◽  
pp. 2150013
Author(s):  
Diem Dang Huan ◽  
Ravi P. Agarwal
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Sufficient Conditions ◽  
Nonlinear Heat Equation ◽  
Index Formula ◽  
Lévy Noise ◽  
Partial Differential ◽  
Stochastic Delay ◽  
Delay Partial Differential Equations ◽  
Levy Noise

This paper aims to investigate the controllability for impulsive neutral stochastic delay partial differential equations (PDEs) driven by fractional Brownian motion (fBm) with Hurst index [Formula: see text] and Lévy noise in Hilbert spaces. By using a fixed point approach without imposing a severe compactness condition on the semigroup, a new set of sufficient conditions is derived. The results in this paper are generalization and continuation of the recent results on this issue. At the end, an application to the stochastic nonlinear heat equation with delays driven by a fBm and Lévy noise is given.

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.

Sign in / Sign up

Export Citation Format

Share Document