RECONSTRUCTION OF THE TIME-DEPENDENT SOURCE TERM IN A STOCHASTIC FRACTIONAL DIFFUSION EQUATION

被引：8
|
作者：
Liu, Chan [1 ]
Wen, Jin [2 ]
Zhang, Zhidong [3 ]
机构：
[1] Fudan Univ, Sch Math Sci, Shanghai 200433, Peoples R China
[2] Northwest Normal Univ, Dept Math, Lanzhou 730070, Gansu, Peoples R China
[3] Sun Yat Sen Univ, Sch Math Zhuhai, Zhuhai 519082, Guangdong, Peoples R China
来源：
INVERSE PROBLEMS AND IMAGING | 2020年 / 14卷 / 06期
基金：
芬兰科学院; 中国国家自然科学基金;
关键词：
Inverse problem; stochastic fractional diffusion equation; random source; Volterra integral equation; mollification; UNKNOWN SOURCE; POTENTIALS; CALCULUS;
D O I：
10.3934/ipi.2020053
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this work, an inverse problem in the fractional diffusion equation with random source is considered. The measurements we use are the statistical moments of the realizations of single point observation u(x(0), t, omega). We build a representation of the solution u in the integral sense, then prove some theoretical results like uniqueness and stability. After that, we establish a numerical algorithm to solve the unknowns, where a mollification method is used.
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页码：1001 / 1024
页数：24
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