Simultaneous identification of initial field and spatial heat source for heat conduction process by optimizations

Advances in Difference Equations

卷:2019

Bin Yang¹  Bingxian Wang¹  Mei Xu¹ 

[1] School of Mathematics Science, Huaiyin Normal University;

关键词: Inverse problem;    Parabolic equation;    Initial field;    Heat source;    Adjoint variational method;    Numerics;   

DOI  :  10.1186/s13662-019-2344-5

来源: DOAJ

【 摘 要 】

Abstract Consider the simultaneous identification of the initial field and spatial heat source for heat conduction process from extra measurements with the two additional measurement data at different times. The uniqueness and conditional stability for this inverse problem are established by using the properties of a parabolic equation and the representation of solution after reforming the equation. By combining the least squares method with the regularization technique, the inverse problem is transformed into an optimal control problem. Based on the existence and uniqueness of the minimizer of the cost functional, an alternative iteration process is built to solve this optimizing problem by the variational adjoint method. The negative gradient direction is selected as the first search direction. For further iterations, the alternative iteration algorithm is used for the initial field and heat source identification. The efficiency of the proposed scheme is tested by the numerical simulation experiments.

【 授权许可】

Unknown