TITLE:
Random Attractors for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities with Additive Noise
AUTHORS:
Jinyan Yin, Yangrong Li, Huijun Zhao
KEYWORDS:
Random Dynamical System; Random Attractor; Hamiltonian Amplitude Equation
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.1 No.3,
September
20,
2013
ABSTRACT: In this
paper, we study the random dynamical system (RDS) generated by the dissipative
Hamiltonian amplitude equation
with additive noise defined on the periodic boundaries. We investigate the
existence of a compact random attractor for the RDS associated with the
equation through introducing two functions and one process in E0=H1×L2.
The compactness of the RDS is
established by the decomposition of solution semigroup.