一类非自治随机阻尼Sine-Gordon方程组的$\mathscr{D}$-拉回吸引子
$\mathscr{D}$-Pullback Attractors for a Class of Non-Autonomous Stochastic Damped Sine-Gordon Equations

研究了带有加法噪音的非自治随机阻尼Sine-Gordon方程组解的渐进行为.运用一致估计证明了$\mathscr{D}$-吸收集的存在性，并由解的分解技巧证明了该动力系统是渐进紧的，从而证明了Sine-Gordon方程组的$\mathscr{D}$-拉回吸引子的存在性.
The asymptotic behavior of the solution to the stochastic damped Sine-Gordon system with additive noise is investigated. Using the Gronwall lemma and the Sobolev embedding theorem, we find that there exists a compact absorption set in the system, which proves the existence of the $\mathscr{D}$-pullback attractor in the Sine-Gordon system