加权空间中非自治随机格点长短波共振方程的渐近行为  

The Asymptotic Behavior of Non-autonomous Stochastic Lattice Long-Wave-Short-Wave Resonance Equations in Weighted Space

作　　者：魏央凡 赵敏[1] 潘陈 熊思洁 WEI Yangfan;ZHAO Min;PAN Chen;XIONG Sijie(College of Mathematics and Physics,Wenzhou University,Wenzhou 325035,Zhejiang)

机构地区：[1]温州大学数理学院,浙江温州325035

出　　处：《丽水学院学报》2025年第2期1-14,共14页Journal of Lishui University

基　　金：国家自然科学基金资助项目“非自治随机Boissonade系统在不同边界条件下的渐近行为”(11801416)。

摘　　要：主要研究无穷格点Z^(N)上具有可乘白噪声的非自治长短波共振方程在加权空间中的渐近行为。首先,通过O-U过程将该方程转化为没有白噪声的随机方程;随后,证明了转化得到的方程生成的非自治随机动力系统在加权空间中的随机吸引子的存在性;最后,得证该随机动力系统在加权空间中的随机指数吸引子的存在性,意味着无白噪声扰动时相应的非自治格点长短波共振方程在加权空间中存在拉回吸引子、拉回指数吸引子。In this paper,we mainly study the asymptotic behavior of the non-autonomous long-wave-short-wave resonance equations with multiplicative white noise on infinite lattices Z^(N) in weighted space.Firstly,we transform the equation into a random equation without white noise through the O-U process.Then,we prove the existence of random attractor for the non-autonomous random dynamical system generated by the transformed equation in weighted space.Finally,we obtain the existence of the random exponential attractor for the random dynamical system in weighted space.These results mean that corresponding non-autonomou lattice long-waveshort-wave resonance equations without white noise disturbance have pullback attractor and pullback exponential attractor in weighted space.

关 键 词：格点长短波共振方程 加权空间 可乘白噪声 随机吸引子 随机指数吸引子 

分 类 号：O175.14[理学—数学]