Galerkin Finite Element Approximation for Semilinear Stochastic Time-Tempered Fractional Wave Equations with Multiplicative Gaussian Noise and Additive Fractional Gaussian Noise

作     者：Yajing Li Yejuan Wang Weihua Deng Daxin Nie 

作者机构：School of Mathematics and StatisticsGansu Key Laboratory of Applied Mathematics and Complex SystemsLanzhou UniversityLanzhou 730000P.R.China College of ScienceNorthwest A&F UniversityYangling 712100ShaanxiP.R.China 

出 版 物：《Numerical Mathematics(Theory,Methods and Applications)》 (高等学校计算数学学报（英文版）)

年 卷 期：2022年第15卷第4期

页      面：1063-1098页

核心收录：

学科分类：07[理学] 070102[理学-计算数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China(Grants No.41875084,11801452,12071195,12225107) the AI and Big Data Funds(Grant No.2019620005000775) the Innovative Groups of Basic Research in Gansu Province(Grant No.22JR5RA391) NSF of Gansu(Grant No.21JR7RA537) 

主　　题：Galerkin finite element method semilinear stochastic time-tempered fractional wave equation fractional Laplacian multiplicative Gaussian noise additive fractional Gaussian noise 

摘      要：To model wave propagation in inhomogeneous media with frequency dependent power-law attenuation,it is needed to use the fractional powers of symmetric coercive elliptic operators in space and the Caputo tempered fractional derivative in *** model studied in this paper is semilinear stochastic space-time fractional wave equations driven by infinite dimensional multiplicative Gaussian noise and additive fractional Gaussian noise,because of the potential fluctuations of the external *** purpose of this work is to discuss the Galerkin finite element approximation for the semilinear stochastic fractional wave ***,the space-time multiplicative Gaussian noise and additive fractional Gaussian noise are discretized,which results in a regularized stochastic fractional wave equation while introducing a modeling error in the mean-square *** further present a complete regularity theory for the regularized equation.A standard finite element approximation is used for the spatial operator,and a mean-square priori estimates for the modeling error and the approximation error to the solution of the regularized problem are ***,numerical experiments are performed to confirm the theoretical analysis.