Differential and Integral Equations

Measure attractor for a stochastic Klein-Gordon-Schrödinger type system

M.N. Poulou and N.B. Zographopoulos

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Abstract

In this paper, we study the long time behavior in the distribution sense of solutions for a stochastic Klein-Gordon-Schrödinger type system, which is defined in a unbounded domain. The existence of one stationary measure from any moment-finite initial data in the space $H^{1}(\mathbb{R})\times H^{1}(\mathbb{R})\times L^{2}(\mathbb{R})$ is proven and then a global measure attractor is constructed consisting of probability measures supported on $H^{2}(\mathbb{R})\times H^{2}(\mathbb{R})\times H^{1}(\mathbb{R}). $

Article information

Source
Differential Integral Equations, Volume 27, Number 5/6 (2014), 489-510.

Dates
First available in Project Euclid: 3 April 2014

Permanent link to this document
https://projecteuclid.org/euclid.die/1396558094

Mathematical Reviews number (MathSciNet)
MR3189530

Zentralblatt MATH identifier
1307.35137

Subjects
Primary: 60F10: Large deviations 60H15: Stochastic partial differential equations [See also 35R60]

Citation

Poulou, M.N.; Zographopoulos, N.B. Measure attractor for a stochastic Klein-Gordon-Schrödinger type system. Differential Integral Equations 27 (2014), no. 5/6, 489--510. https://projecteuclid.org/euclid.die/1396558094


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