Data compatibility and conditional stability for an inverse source problem in the heat equation

被引：42

作者：

Li, GS ^{[1
]}

机构：

[1] Shandong Univ Technol, Inst Appl Math, Sch Math & Informat Sci, Shandong 255049, Peoples R China

来源：

APPLIED MATHEMATICS AND COMPUTATION | 2006年 / 173卷 / 01期

基金：

中国国家自然科学基金;

关键词：

inverse problem of nonlinear source term; integral identity method; data compatibility; conditional stability;

D O I：

10.1016/j.amc.2005.04.053

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

An inverse problem of determining a nonlinear source term in a heat equation via final observations is investigated. By applying integral identity method, data compatibilities are obtained with which the inverse source problem here is proved to be solvable. Furthermore, with aid of an integral identity that connects unknown source terms with the known data, a conditional stability is constructed. Theoretical examples are presented showing that theorems and conclusions given in this paper are reasonable and practicable. (c) 2005 Elsevier Inc. All rights reserved.

引用

页码：566 / 581

页数：16

共 14 条

[1] Structural identification of an unknown source term in a heat equation [J].

Cannon, JR ;

DuChateau, P .

INVERSE PROBLEMS, 1998, 14 (03) :535-551

[2]

CANNON JR, 1984, ENCY MATH ITS APPL, V23

[3] An inverse parabolic problem with non-zero initial condition [J].

Choulli, M ;

Yamamoto, M .

INVERSE PROBLEMS, 1997, 13 (01) :19-27

[4]

DUCHATEAU P, 1995, SIAM J MATH ANAL, V26, P1473, DOI 10.1137/S0036141093259257

[5] An existence result for an inverse problem for a quasilinear parabolic equation [J].

Gatti, S .

INVERSE PROBLEMS, 1998, 14 (01) :53-65

[6] Some inverse problems for the diffusion equation [J].

Isakov, V .

INVERSE PROBLEMS, 1999, 15 (01) :3-10

[7]

Isakov V., 2006, Inverse Problems for Partial Differential Equations

[8]

LI GS, 2003, J INVERSE ILL-POSE P, V11, P371

[9]

Lions J.-L., 1971, OPTIMAL CONTROL SYST

[10] AN INVERSE PROBLEM FOR A SEMILINEAR PARABOLIC EQUATION [J].

LORENZI, A .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1982, 131 :145-166

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