Integral equations for shape and impedance reconstruction in corrosion detection

Inverse Problems

Volumn 26, Issue 9, 2010, Pages

  Cakoni, Fioralba ^a   Kress, Rainer ^b   Schuft, Christian ^b  

^a UNIVERSITY OF DELAWARE   (United States)

^b UNIVERSITY OF GÖTTINGEN   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY CURVES; CAUCHY DATA; CORROSION DETECTION; EXACT SOLUTION; HARMONIC FUNCTION; ILL POSED; IMPEDANCE BOUNDARY CONDITIONS; IMPEDANCE FUNCTIONS; INJECTIVITY; LINEARIZED SYSTEMS; MATHEMATICAL FOUNDATIONS; NUMERICAL RECONSTRUCTION; PLANAR DOMAIN;

CURVE FITTING; DIFFERENTIAL EQUATIONS; FOURIER SERIES; HARMONIC ANALYSIS; HARMONIC FUNCTIONS; INTEGRAL EQUATIONS; LINEARIZATION; NONLINEAR EQUATIONS; SOIL STRUCTURE INTERACTIONS;

INVERSE PROBLEMS;

EID: 78049327320     PISSN: 02665611     EISSN: 13616420     Source Type: Journal    
DOI: 10.1088/0266-5611/26/9/095012     Document Type: Article

References (31)

1. Alessandrini G. Del Piero L and Rondi L 2003 Stable determination of corrosion by a single electrostatic boundary measurement Inverse Problems 19 973-84
2. Alessandrini G, Rondi L, Rosset E and Vessella S 2009 The stability for the Cauchy problem for elliptic equations 57 Inverse Problems 25 123004
3. Alessandrini G and Sincich E 2007 Solving elliptic Cauchy problems and the identification of nonlinear corrosion J. Comput. Appl. Math. 198 307-20
4. Andrieux S, Baranger T and Abda A B 2006 Solving Cauchy problems by minimizing an energy-like functional Inverse problems 22 115-33
5. Bacchelli V 2009 Uniqueness for the determination of unknown boundary and impedance with the homogeneous Robin condition inverse Problems 25 4
6. Cakoni F, Colton D and Monk P 2001 The direct and inverse scattering problem for partially coated obstacles Inverse Problems 17 1997-2015
7. Cakoni F and Kress R 2007 Integral equations for inverse problems in corrosion detection from partial Cauchy data Inverse Problems Imaging 1 229-45
8. Chaabane S and Jaoua M 1999 Identification of Robin coefficients by means of boundary measurements Inverse Problems 15 1425-38
9. Choulli M 2004 An inverse problem in corrosion detection: stability extimates J. Inverse III-Posed Problems 12 349-67
10. Costabel M and DaugeM 1996 A singularly perturbed mixed boundary value problem Commun. Partial Differ. Equ. 21 1919-49
11. Eckel H and Kress R 2007 Nonlinear integral equations for the inverse electrical impedance problem Inverse Pmblems 23 475-91
12. Elliott D 1998 Sigmoidal transformations and the trapezoidal rule J. Aust. Math. Soc. B 40 E77-137
13. Elschner J and Graham I 1995 An optimal order collocation method for first kind boundary integral equations on polygons Numer. Math. 70 1-31
14. Fasino D and Inglese G 2007 Recovering nonlinear terms in an inverse boundary value problem for Laplace's equation: a stability estimate J. Comput. Appl. Math. 198 460-70
15. Grisvard P 1985 Elliptic Problems in Nonsmooth Domains (Boston. MA: Pitman)
16. Hsiao G and Wendland W 1979 On the integral equation method for the plane mixed boundary value problem of the Laplacian Math. Methods Appl. Sci. 1 265-321
17. Inglese G 1997 An inverse problem in corrosion detection Inverse Problems 13 977-94
18. Ivanyshyn O 2007 Nonlinear boundary integral equations in inverse scattering PhD Thesis Universität Göttingen
19. Kaup P G and Santosa F 1995 Nondestructive evaluation of corrosion damage using electrostatic measurements J. Nondestr. Eval. 14 127-36
20. Kaup P G. Santosa F and Vogelius M 1996 Method for imaging corrosion damage in thin plates from electrostatic data Inverse Problems 12 279-93
21. Kirsch A 1996 An Intmduction to the Mathematical Theory of Inverse Problems (Berlin: Springer)
22. Korobov N M 1963 Number Theoretic Methods of Approximate Analysis (Moscow: Fizmatgiz)
23. Kress R 1990 A Nyström method for boundary integral equations in domains with corners Numer. Math. 58 145-61
24. Kress R 1999 Linear Integral Equations 2nd edn (New York: Springer)
25. Kress R and Rundell W 2005 Nonlinear integral equations and the iterative solution for an inverse boundary value problem Inverse Problems 21 1207-23
26. McLean W 2000 Strongly Elliptic Systems and Boundaiy Integral Equations (Cambridge: Cambridge University Press)
27. Pagani C D and Pierotti D 2009 Identifiability problems of defects with the Robin condition Inverse Problems 25 12
28. Potthast R 1994 Fréchet differentiability of boundary integral operators in inverse acoustic scattering Inverse Problems 10 431-47
29. Rundell W 2008 Recovering an obstacle and its impedance from Cauchy data Inveise Problems 24 045003
30. Vogt A 2001 Analytische und numerische Untersuchung von direkten und inversen Randwertproblemen in Gebieten mit Ecken mittels Integralgleichungsmethoden PhD Thesis Universität Göttingen
31. Yan Y and Sloan I 1988 On integral equations of the first kind with logarithmic kernels J. Integral Equ. Appl. 1 549-79