Dynamics of non-autonomous stochastic dissipative Hamiltonian amplitude wave equations with rapidly oscillating force. Issue 4 (12th March 2019) - Yin, Jinyan; Li, Yangrong; She, Lianbing
ABSTRACT: This paper considers the limiting behavior of pullback attractors for the non-autonomous stochastic dissipative Hamiltonian amplitude wave equation with rapidly oscillating forceg ϵ ( x, t ) defined on a real line. The presence of the complex valued termi u x brings some difficulties even to prove the induced system is pullback absorbing. Thus, by choosing a new numberδ > 0, some new uniform asymptotic estimates are used to prove the existence of pullback attractors inH 1 ( R ) × L 2 ( R ), as well as to show the upper semicontinuity of the family of oscillating attractors wheng ϵ ( x, t ) tends to the averageg 0 ( x, t ) as the density of noiseϵ approaches to zero.