Dynamics of non-autonomous stochastic dissipative Hamiltonian amplitude wave equations with rapidly oscillating force

摘要

This paper considers the limiting behavior of pullback attractors for the non-autonomous stochastic dissipative Hamiltonian amplitude wave equation with rapidly oscillating force g epsilon (x, t) defined on a real line. The presence of the complex valued term iu(x) brings some difficulties even to prove the induced system is pullback absorbing. Thus, by choosing a new number delta 0, some new uniform asymptotic estimates are used to prove the existence of pullback attractors in H-1(R) x L-2(R), as well as to show the upper semicontinuity of the family of oscillating attractors when g(epsilon)(x, t) tends to the average g(0)(x, t) as the density of noise epsilon approaches to zero.