文献类型：期刊文献

英文题名：Sensitivity analysis of the non-linear Fokker-Planck equations with uncertainty

作者：Liao, Jie[1];Liu, Hui[1]

机构：[1]East China Univ Sci & Technol, Sch Math, Shanghai 200237, Peoples R China

年份：2022

卷号：64

外文期刊名：NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS

收录：;EI(收录号：20214411091118);WOS:【SCI-EXPANDED(收录号:WOS:000715046500002)】；

基金：The authors would like to acknowledge many valuable discussions with Professor Xiongfeng Yang for this project. This research is partially supported by National Natural Science Foundation of China (Grant Nos. 11871335 and 11971008) .

语种：英文

外文关键词：Non-linear Fokker-Planck equation; Sensitivity analysis; Random input; Uniform-in-time estimates

摘要：In this paper, we study sensitivity analysis of the non-linear Fokker-Planck equations with uncertainty. Modeled by random variable, the uncertainty enters the solution through initial data. By deriving Lyapunov-type inequalities, under some smallness assumptions on the initial data, we have the regularity of the solution in the random space. The nonlinearity in the model brings new difficulties to the energy estimates, which is resolved by using careful weighted-in-v energy estimates suitable for Fokker-Planck operators. The analysis is important for understanding of the sensitivity of the system under random perturbations, and for the study of convergence rates of popular numerical methods for uncertainty quantification based on polynomial chaos expansions. (C) 2021 Elsevier Ltd. All rights reserved.