Determination of a term in the right-hand side of parabolic equations

被引：24

作者：

Dinh Nho Hao ^{[1
]}

Bui Viet Huong ^{[2
]}

Nguyen Thi Ngoc Oanh ^{[2
]}

Phan Xuan Thanh ^{[3
]}

机构：

[1] VAST, Hanoi Inst Math, 18 Hoang Quoc Viet Rd, Hanoi, Vietnam

[2] Thai Nguyen Univ, Coll Sci, Thai Nguyen, Vietnam

[3] Hanoi Univ Sci & Technol, Sch Appl Math & Informat, 1 Dai Co Viet Rd, Hanoi, Vietnam

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2017年 / 309卷

关键词：

Inverse source problems; Integral observations; Least squares method; Tikhonov regularization; Finite element method; Conjugate gradient method; NONCHARACTERISTIC CAUCHY-PROBLEM; OVERSPECIFIED BOUNDARY DATA; INVERSE SOURCE PROBLEM; HEAT-EQUATIONS; OVERDETERMINATION CONDITION; DIFFERENTIAL-EQUATIONS; CONDITIONAL STABILITY; VARIATIONAL METHOD; POINT SOURCES; IDENTIFICATION;

D O I：

10.1016/j.cam.2016.05.022

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The inverse problem of determining a term in the right hand side of parabolic equations from integral observations is investigated. The observations can be regarded as generalized interior point observations which are collected in practice. The problem is then reformulated as a least squares problem in coupling with a Tikhonov regularization term. It is proved that the Tikhonov functional is Frechet differentiable and a formula for the gradient is derived via an adjoint problem. The variational problem is discretized by the finite element method, the convergence of which is proved. The discretized variational problem is numerically solved by the conjugate gradient method. Some numerical examples are presented for showing the efficiency of the method. (C) 2016 Elsevier B.V. All rights reserved.

引用

页码：28 / 43

页数：16

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