Random Attractors for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities with Additive Noise ()
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.
Share and Cite:
Yin, J. , Li, Y. and Zhao, H. (2013) Random Attractors for the Dissipative Hamiltonian Amplitude Equation Governing Modulated Wave Instabilities with Additive Noise.
Journal of Applied Mathematics and Physics,
1, 37-46. doi:
10.4236/jamp.2013.13007.
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