THE REGULARIZED SOLUTION APPROXIMATION OF FORWARD/BACKWARD PROBLEMS FOR A FRACTIONAL PSEUDO-PARABOLIC EQUATION WITH RANDOM NOISE  

作　　者：狄华斐 容伟杰 Huafei DI;Weijie RONG(School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China;Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes,Guangzhou University,Guangzhou,510006,China)

机构地区：[1]School of Mathematics and Information Science,Guangzhou University,Guangzhou,510006,China [2]Key Laboratory of Mathematics and Interdisciplinary Sciences of Guangdong Higher Education Institutes,Guangzhou University,Guangzhou,510006,China

出　　处：《Acta Mathematica Scientia》2023年第1期324-348,共25页数学物理学报（B辑英文版）

基　　金：supported by the Natural Science Foundation of China(11801108);the Natural Science Foundation of Guangdong Province(2021A1515010314);the Science and Technology Planning Project of Guangzhou City(202201010111)。

摘　　要：This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.

关 键 词：regularized solution approximation forward/backward problems fractional Laplacian Gaussian white noise Fourier truncation method 

分 类 号：O17[理学—数学]