Identification of two coefficients with data of one component for a nonlinear parabolic system

被引：17

作者：

Cristofol, Michel ^{[1
]}

Gaitan, Patricia ^{[1
]}

Ramoul, Hichem ^{[2
]}

Yamamoto, Masahiro ^{[3
]}

机构：

[1] Lab Anal, F-13453 Marseille, France

[2] Univ Badji Mokhtar, Dept Math, LMA, Annaba 23000, Algeria

[3] Univ Tokyo, Dept Math, Meguro Ku, Tokyo 153, Japan

来源：

APPLICABLE ANALYSIS | 2012年 / 91卷 / 11期

关键词：

parabolic systems; inverse problem; Carleman estimate; Lipschitz stability estimate; INVERSE PROBLEM; GLOBAL UNIQUENESS; TERM;

D O I：

10.1080/00036811.2011.583240

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this article, we consider a nonlinear parabolic system with two components and prove a stability estimate of Lipschitz type in determining two coefficients of the system by data of only one component. The main idea for the proof is a Carleman estimate.

引用

收藏

页码：2073 / 2081

页数：9

相关论文

共 19 条

[1]

[Anonymous], 1968, LINEAR QUASILINEAR E

[2] A new Carleman inequality for parabolic systems with a single observation and applications [J].

Benabdallah, Assia ;

Cristofol, Michel ;

Gaitan, Patricia ;

de Teresa, Luz .

COMPTES RENDUS MATHEMATIQUE, 2010, 348 (1-2) :25-29

[3] Inverse problem for a parabolic system with two components by measurements of one component [J].

Benabdallah, Assia ;

Cristofol, Michel ;

Gaitan, Patricia ;

Yamamoto, Masahiro .

APPLICABLE ANALYSIS, 2009, 88 (05) :683-709

[4] Stable determination of a semilinear term in a parabolic equation [J].

Choulli, M ;

Ouhabaz, EM ;

Yamamoto, M .

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2006, 5 (03) :447-462

[5]

Cristofol M., COMP REND ACAD UNPUB

[6]

Cristofol M., 2011, COMMU PURE IN PRESS

[7] Inverse problems for a 2x2 reaction-diffusion system using a Carleman estimate with one observation [J].

Cristofol, Michel ;

Gaitan, Patricia ;

Ramoul, Hichem .

INVERSE PROBLEMS, 2006, 22 (05) :1561-1573

[8] UNICITY IN AN INVERSE PROBLEM FOR AN UNKNOWN REACTION TERM IN A REACTION DIFFUSION EQUATION [J].

DUCHATEAU, P ;

RUNDELL, W .

JOURNAL OF DIFFERENTIAL EQUATIONS, 1985, 59 (02) :155-164

[9] Global uniqueness and Holder stability for recovering a nonlinear source term in a parabolic equation [J].

Egger, H ;

Engl, HW ;

Klibanov, MV .

INVERSE PROBLEMS, 2005, 21 (01) :271-290

[10] Global Carleman inequalities for parabolic systems and applications to controllability [J].

Fernandez-Cara, Enrique ;

Guerrero, Sergio .

SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2006, 45 (04) :1395-1446