Lipschitz stability of a non-standard problem for the non-stationary transport equation via a Carleman estimate

Inverse Problems

Volumn 22, Issue 3, 2006, Pages 881-890

  Klibanov, Michael V ^a   Pamyatnykh, Sergey E ^a  

^a UNIVERSITY OF NORTH CAROLINA AT CHARLOTTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY ELEMENT METHOD; CONVERGENCE OF NUMERICAL METHODS; INVERSE PROBLEMS; MATHEMATICAL MODELS; PROBLEM SOLVING; THEOREM PROVING;

LIPSCHITZ STABILITY; NON-STATIONARY TRANSPORT EQUATIONS; SINGLE-SPEED TRANSPORT; UNIQUENESS;

DIFFERENCE EQUATIONS;

EID: 33744541833     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/22/3/009     Document Type: Article

References (11)

1. Ames K A and Straughan B 1997 Non-Standard and Improperly Posed Problems (Cambridge: Academic)
2. 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
3. Carleman T 1939 Sur un problème d'unicité pour les systèmes d'équations aux dérivées partielles deux variables indépendantes Ark. Mat. Astr. Fys. B 26 1-9
4. Case K M and Zweifel P F 1967 Linear Transport Theory (Reading, MA: Addison-Wesley)
5. Hörmander L 1963 Linear Partial Differential Operators (Berlin: Springer)
6. Isakov V 1998 Inverse Problems for Partial Differential Equations (New York: Springer)
7. Kazemi M and Klibanov M V 1993 Stability estimates for ill-posed Cauchy problem involving hyperbolic equations and inequalities Appl. Anal. 50 93-102
8. Klibanov M V and Malinsky J 1991 Newton-Kantorovich method for 3-dimensional potential inverse scattering problem and stability of the hyperbolic Cauchy problem with time dependent data Inverse Problems 7 577-95
9. Klibanov M V and Timonov A 2004 Carleman Estimates for Coefficient Inverse Problems and Numerical Applications (Utrecht: VSP) www.vsppub.com
10. Lavrentev M M, Romanov V G and Shishatskii S P 1986 Ill-Posed Problems of Mathematical Physics and Analysis (Translations of Mathematical Monographs vol 64) (Providence, RI: American Mathematical Society)
11. Prilepko A I and Ivankov A L 1985 Inverse problems for the determination of a coefficient and the right side of a non-stationary multivelocity transport equation with overdetermination at a point Diff. Eqns 21 88-96