Dynamics of non-autonomous stochastic dissipative Hamiltonian amplitude wave equations with rapidly oscillating force. Issue 4 (12th March 2019)

• Record Type: Journal Article
• Authors: Yin, Jinyan; Li, Yangrong; She, Lianbing
• Is Part Of: Applicable analysis. Volume 98:Issue 4(2019)
• Page Start: 693
• Page End: 717
• Publication Date: 2019-03-12
• Subjects: Hamiltonian amplitude equation -- rapidly oscillating force -- upper semicontinuity -- random attractor -- unbounded domain; 35B40 -- 37L55 -- 60H15; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2017.1400534
• Languages: English
• ISSNs: 0003-6811

Abstract

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.