Differential and Integral Equations

Dynamics of stochastic Klein--Gordon--Schrödinger equations in unbounded domains

Boling Guo, Yan Lv, and Xiaoping Yang

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Abstract

The long-time behavior in the sense of distributions for stochastic Klein--Gordon--Schrödinger equations in the whole space ${\mathbb R}^n$, $1\leq n\leq 3$, is studied. First the existence of one stationary measure from any moment-finite initial data in the space $H^1({\mathbb R}^n)\times H^1({\mathbb R}^n) \times L^2({\mathbb R}^n)$ is proved and then a global measure attractor is constructed in the space consisting of probability measures supported on $H^2({\mathbb R}^n)\times H^2({\mathbb R}^n)\times H^1({\mathbb R}^n)$. Because of the lack of compact embedding, some a priori estimates and a split of solutions play important roles in the approach.

Article information

Source
Differential Integral Equations, Volume 24, Number 3/4 (2011), 231-260.

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356019032

Mathematical Reviews number (MathSciNet)
MR2757459

Zentralblatt MATH identifier
1240.60187

Subjects
Primary: 60F10: Large deviations 60H15: Stochastic partial differential equations [See also 35R60] 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]

Citation

Lv, Yan; Guo, Boling; Yang, Xiaoping. Dynamics of stochastic Klein--Gordon--Schrödinger equations in unbounded domains. Differential Integral Equations 24 (2011), no. 3/4, 231--260. https://projecteuclid.org/euclid.die/1356019032


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