Carleman estimates for a stochastic degenerate parabolic equation and applications to null controllability and an inverse random source problem

被引：12
|
作者：
Wu, Bin [1 ]
Chen, Qun [1 ]
Wang, Zewen [2 ]
机构：
[1] Nanjing Univ Informat Sci & Technol, Sch Math & Stat, Nanjing 210044, Peoples R China
[2] East China Univ Technol, Sch Sci, Nanchang 330013, Jiangxi, Peoples R China
来源：
INVERSE PROBLEMS | 2020年 / 36卷 / 07期
基金：
中国国家自然科学基金;
关键词：
stochstic degenerate parabolic equation; Carleman estimate; null controllability; inverse random source problem; UNIQUE CONTINUATION; OPERATORS; SYSTEM; OBSERVABILITY;
D O I：
10.1088/1361-6420/ab89c3
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper, we establish two Carleman estimates for a stochastic degenerate parabolic equation. The first one is for the backward stochastic degenerate parabolic equation with singular weight function. Combining this Carleman estimate and an approximate argument, we prove the null controllability of the forward stochastic degenerate parabolic equation with the gradient term. The second one is for the forward stochastic degenerate parabolic equation with regular weighted function, based on which we obtain the Lipschitz stability for an inverse problem of determining a random source depending only on time in the forward stochastic degenerate parabolic equation.
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页数：38
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