Inverse problems for a 2 × 2 reaction-diffusion system using a Carleman estimate with one observation

Inverse Problems

Volumn 22, Issue 5, 2006, Pages 1561-1573

  Cristofol, Michel ^a,b   Gaitan, Patricia ^a,b   Ramoul, Hichem ^c  

^a AIX MARSEILLE UNIVERSITÉ   (France)

^b AIX MARSEILLE UNIVERSITY   (France)

^c ABBES LAGHROUR UNIVERSITY   (Algeria)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CONDITIONS; DIFFUSION; PARAMETER ESTIMATION; PROBLEM SOLVING;

CARLEMAN ESTIMATE; REACTION-DIFFUSION SYSTEM;

INVERSE PROBLEMS;

EID: 33749011180     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/5/003     Document Type: Article

References (21)

1. Ammar Khodja F, Benabdallah A, Dupaix C and Kostine I 2005 Null controllability of some systems of parabolic type by one control force ESAIM: COCV 11 426-48
2. Baudouin L and Puel J P 2002 Uniqueness and stability in an inverse problem for the Schrödinger equation Inverse Problems 18 1537-54
3. Brezis H 1983 Analyse fonctionnelle (Paris: Masson)
4. Bukhgeim A L 1999 Volterra Equations and Inverse Problems (Inverse and Ill-Posed Problems Series) (Utrecht: VSP)
5. Bukhgeim A L and Klibanov M V 1981 Uniqueness in the large of a class of multidimensional inverse problems Sov. Math. Dokl. 17 244-7
6. Cannon J R and Duchateau P 1998 Structural identification of an unknown source term in a heat equation Inverse Problems 14 535-51
7. Chakrabarty S P and Hanson F B 2005 Optimal control of drug delivery to brain tumors for a distributed parameters model Proc. 2005 American Control Conference pp 973-8
8. Fursikov A 2000 Optimal Control of Distributed Systems (Translations of Mathematical Monographs vol 187) (Providence, RI: American Mathematical Society)
9. Isakov V 1998 Inverse Problems for Partial Differential Equations (Berlin: Springer)
10. Imanuvilov O Yu and Yamamoto M 1998 Lipschitz stability in inverse problems by Carleman estimates Inverse Problems 14 1229-45
11. Imanuvilov O Yu, Isakov V and Yamamoto M 2003 An inverse problem for the dynamical Lamé system with two sets of boundary data CPAM 56 1366-82
12. Klibanov M V 1984 Inverse problems in the 'large' and Carleman bounds Diff. Eqns 20 755-60
13. Klibanov M V 1992 Inverse problems and Carleman estimates Inverse Problems 8 575-96
14. Klibanov M V 2006 Estimates of initial conditions of parabolic equations and inequalities via lateral Cauchy data Inverse Problems 22 495-514
15. Klibanov M V and Timonov A 2004 Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Inverse and Ill-Posed Series) (Utrecht: VSP)
16. Lions J L 1968 Contrle Optimal de Systèmes Gouvernés par des quations aux Dérivées Partielles (Paris: Dunod)
17. Murray J D 1989 Mathematical Biology (Berlin: Springer)
18. Puel J-P and Yamamoto M 1996 On a global estimate in a linear inverse hyperbolic problem Inverse Problems 12 995-1002
19. Smoller J 1983 Shock Waves and Reaction-Diffusion Equations (Berlin: Springer)
20. Turing A M 1952 The chemical basis of morphogenesis Phil. Trans. R. Soc. B 237 37-72
21. Yamamoto M and Zou J 2001 Simultaneous reconstruction of the initial temperature and heat radiative coefficient Inverse Problems 17 1181-202