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Random dynamics of p-Laplacian lattice systems driven by infinite-dimensional nonlinear noise
Stochastic Processes and their Applications ( IF 1.4 ) Pub Date : 2020-12-01 , DOI: 10.1016/j.spa.2020.08.002
Renhai Wang , Bixiang Wang

Abstract This article is concerned with the global existence and random dynamics of the non-autonomous p -Laplacian lattice system defined on the entire integer set driven by infinite-dimensional nonlinear noise. The existence and uniqueness of mean square solutions to the equations are proved when the nonlinear drift and diffusion terms are locally Lipschitz continuous. It is shown that the mean random dynamical system generated by the solution operators has a unique tempered weak pullback random attractor in a Bochner space. The existence of invariant measures for the stochastic equations in the space of square summable sequences is also established. The idea of uniform tail-estimates of solutions is employed to show the tightness of a family of distribution laws of the solutions.

中文翻译:

由无限维非线性噪声驱动的 p-Laplacian 晶格系统的随机动力学

摘要 本文关注由无限维非线性噪声驱动的在整个整数集上定义的非自治p-拉普拉斯晶格系统的全局存在性和随机动力学。当非线性漂移项和扩散项局部Lipschitz连续时,证明了方程均方解的存在唯一性。结果表明,由求解算子生成的平均随机动力系统在 Bochner 空间中具有独特的缓和弱回拉随机吸引子。还建立了平方可和序列空间中随机方程的不变测度的存在性。采用解的统一尾估计的思想来显示解的分布规律族的紧密性。
更新日期:2020-12-01
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