ABSTRACT
This paper considers the limiting behavior of pullback attractors for the non-autonomous stochastic dissipative Hamiltonian amplitude wave equation with rapidly oscillating force defined on a real line. The presence of the complex valued term
brings some difficulties even to prove the induced system is pullback absorbing. Thus, by choosing a new number
, some new uniform asymptotic estimates are used to prove the existence of pullback attractors in
, as well as to show the upper semicontinuity of the family of oscillating attractors when
tends to the average
as the density of noise
approaches to zero.
Acknowledgements
The authors would like to thank the referees for carefully reading the manuscript and valuable suggestions which lead to an improvement of this paper.
Notes
No potential conflict of interest was reported by the authors.