具有快速振荡项的非自治随机p-Laplace方程随机吸引子的上半连续性
发布时间：2018-12-12 20:23
【摘要】：本文主要研究定义在Rn上的具有快速震荡项的非自治带可乘白噪音的随机p-Laplace方程吸引子的上半连续性;借助解的尾部估计,证明了定义在无界域上该系统的拉回渐近紧性.本文考虑如下快速震荡具可乘白噪音的p-Laplace方程(?)其中,tT,τ∈R,p2和λ0为常数,gε(x,t)为快速震荡外力,W(t)表示双边实值Wiener过程.本文共有四章:第一章,介绍随机动力系统、随机吸引子及p-Laplace方程的背景及研究现状,说明本文的主要研究内容;给出本论文所需要的一些基础理论知识:相关定义和引理.第二章,通过O-U变换消去随机项,将上述随机微分方程转化为带随机参数的确定性方程,然后用Galerkin逼近的方法得到解的存在唯一性以说明该p-Laplace方程生成一个随机动力系统.第三章,给出随机P-Laplace方程解的一致估计,并结合Sobolev紧嵌入定理得到系统在L2(Rn)空间中的渐近紧性,证明系统在L2(Rn)空间存在唯一的随机吸引子.第四章,通过证明随机动力系统在L2空间上的收敛性,得到随机吸引子的上半连续性.
[Abstract]:In this paper, we mainly study the upper semicontinuity of the attractor of the stochastic p-Laplace equation with fast oscillatory terms defined on Rn with multiplicative white noise, and prove the tension asymptotically compactness of the system defined in unbounded domain by means of the tail estimation of the solution. In this paper, we consider the following p-Laplace equations of fast oscillation with multiplicative white noise (?) Where tT, 蟿 鈭，
本文编号：2375193
[Abstract]:In this paper, we mainly study the upper semicontinuity of the attractor of the stochastic p-Laplace equation with fast oscillatory terms defined on Rn with multiplicative white noise, and prove the tension asymptotically compactness of the system defined in unbounded domain by means of the tail estimation of the solution. In this paper, we consider the following p-Laplace equations of fast oscillation with multiplicative white noise (?) Where tT, 蟿 鈭，
本文编号：2375193
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