带乘性噪声的时滞随机Kuramoto-Sivashinsky方程吸引子的存在
Pullback Attractors for Delay Non-Autonomous Stochastic Kuramoto-Sivashinsky Equation with Multiplicative Noise
DOI: 10.12677/PM.2022.127134, PDF,   
作者: 徐智恒：伊犁师范大学应用数学研究所，新疆 伊犁；刁玉存：伊犁师范大学数学与统计学院，新疆 伊犁
关键词: 时滞随机Kuramoto-Sivashinsky方程；随机吸引子；渐近紧性；乘性噪声；Delay Non-Autonomous Stochastic Kuramoto-Sivashinsky Equation； Pullback Attractors； Asymptotic Compactness； Multiplicative Noise
摘要: 本文研究了带有乘性噪声的非自治随机时滞Kuramoto-Sivashinsky方程解的长时间行为。通过对解的一致估计，结合随机吸引子的存在性定理，证明了由该方程C([−ρ,0],L2(I))所生成的随机动力系统吸引子的存在性。
Abstract: In this paper, we study the long time behavior of delay non-autonomous stochastic Kuramoto- Sivashinsky equation with multiplicative noise. We prove the existence of pullback attractors in the space C([−ρ,0],L2(I)) for the dynamical system generated by the equation above, by some uniform estimation, together with the existence theorem of pullback attractors.
文章引用：徐智恒, 刁玉存. 带乘性噪声的时滞随机Kuramoto-Sivashinsky方程吸引子的存在[J]. 理论数学, 2022, 12(7): 1223-1230. https://doi.org/10.12677/PM.2022.127134

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