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Volumn 198, Issue 2, 2007, Pages 307-320

Solving elliptic Cauchy problems and the identification of nonlinear corrosion

Author keywords

Cauchy problem; Corrosion; Inverse boundary problem

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; CORROSION; INVERSE PROBLEMS;

EID: 33748750897     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2005.06.048     Document Type: Article
Times cited : (23)

References (20)
  • 2
    • 84988863508 scopus 로고    scopus 로고
    • G. Alessandrini, E. Sincich, Detecting nonlinear corrosion by electrostatic measurements, Appl. Anal. 85(1-3) (2006) 107-128.
  • 3
    • 0343772980 scopus 로고    scopus 로고
    • Numerical solution of a Cauchy problem for the Laplace equation
    • Berntsson F., and Eldén L. Numerical solution of a Cauchy problem for the Laplace equation. Inverse Problems 17 (2001) 839-853
    • (2001) Inverse Problems , vol.17 , pp. 839-853
    • Berntsson, F.1    Eldén, L.2
  • 4
    • 0036902102 scopus 로고    scopus 로고
    • Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling
    • Bryan K., and Vogelius M. Singular solutions to a nonlinear elliptic boundary value problem originating from corrosion modeling. Quart. Appl. Math. 60 (2002) 675-694
    • (2002) Quart. Appl. Math. , vol.60 , pp. 675-694
    • Bryan, K.1    Vogelius, M.2
  • 6
    • 1542356611 scopus 로고    scopus 로고
    • Computation for multidimensional Cauchy problem
    • Cheng J., Hon Y.C., and Wei T. Computation for multidimensional Cauchy problem. SIAM J. Control Optim. 42 (2003) 381-396
    • (2003) SIAM J. Control Optim. , vol.42 , pp. 381-396
    • Cheng, J.1    Hon, Y.C.2    Wei, T.3
  • 7
    • 0035518988 scopus 로고    scopus 로고
    • A Mann iterative regularization method for elliptic Cauchy problems
    • Engl H.W., and Leitão A. A Mann iterative regularization method for elliptic Cauchy problems. Numer. Funct. Anal. Optim. 22 (2001) 861-884
    • (2001) Numer. Funct. Anal. Optim. , vol.22 , pp. 861-884
    • Engl, H.W.1    Leitão, A.2
  • 9
    • 0342572571 scopus 로고    scopus 로고
    • The Cauchy problem for Laplace's equation via the conjugate gradient method
    • Hào D.N., and Lesnic D. The Cauchy problem for Laplace's equation via the conjugate gradient method. IMA J. Appl. Math. 65 (2000) 199-217
    • (2000) IMA J. Appl. Math. , vol.65 , pp. 199-217
    • Hào, D.N.1    Lesnic, D.2
  • 10
    • 33748745968 scopus 로고    scopus 로고
    • An optimization algorithm for solving the Cauchy problem for an elliptic equation
    • Kabanikhin S.I., and Karchevskiǐ A.L. An optimization algorithm for solving the Cauchy problem for an elliptic equation. Dokl. Akad. Nauk. 359 (1998) 445-447
    • (1998) Dokl. Akad. Nauk. , vol.359 , pp. 445-447
    • Kabanikhin, S.I.1    Karchevskiǐ, A.L.2
  • 11
    • 0037229004 scopus 로고    scopus 로고
    • On the existence and blow-up of solutions of a two dimensional nonlinear boundary value problem arising in corrosion modeling
    • Kavian O., and Vogelius M. On the existence and blow-up of solutions of a two dimensional nonlinear boundary value problem arising in corrosion modeling. Proc. Roy. Soc. Edinburgh 133A (2003) 119-149
    • (2003) Proc. Roy. Soc. Edinburgh , vol.133 A , pp. 119-149
    • Kavian, O.1    Vogelius, M.2
  • 13
    • 0000710664 scopus 로고
    • On iterative procedure for solving ill-posed boundary value problems that preserve differential equations
    • Kozlov V.A., and Maz'ya V.G. On iterative procedure for solving ill-posed boundary value problems that preserve differential equations. Leningrad Math. J. 1 (1990) 1207-1228
    • (1990) Leningrad Math. J. , vol.1 , pp. 1207-1228
    • Kozlov, V.A.1    Maz'ya, V.G.2
  • 15
    • 0034250874 scopus 로고    scopus 로고
    • An iterative method for solving elliptic Cauchy problem
    • Leitão A. An iterative method for solving elliptic Cauchy problem. Numer. Funct. Anal. Optim. 21 (2000) 715-742
    • (2000) Numer. Funct. Anal. Optim. , vol.21 , pp. 715-742
    • Leitão, A.1
  • 16
    • 33748744277 scopus 로고    scopus 로고
    • J.L. Lions, E. Magenes, Non-Homogeneous Boundary Value Problems and Applications, vol.1, Springer, Berlin, 1972.
  • 17
    • 3242796795 scopus 로고    scopus 로고
    • Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation
    • Marin L., Elliott L., Heggs P.J., Ingham D.B., Lesnic D., and Wen X. Comparison of regularization methods for solving the Cauchy problem associated with the Helmholtz equation. Internat. J. Numer. Methods Eng. 60 (2004) 1933-1947
    • (2004) Internat. J. Numer. Methods Eng. , vol.60 , pp. 1933-1947
    • Marin, L.1    Elliott, L.2    Heggs, P.J.3    Ingham, D.B.4    Lesnic, D.5    Wen, X.6
  • 18
    • 0037053182 scopus 로고    scopus 로고
    • Boundary element solution of the Cauchy problem in linear elasticity using singular value decomposition
    • Marin L., and Lesnic D. Boundary element solution of the Cauchy problem in linear elasticity using singular value decomposition. Comput. Methods Appl. Mech. Eng. 191 (2002) 3257-3270
    • (2002) Comput. Methods Appl. Mech. Eng. , vol.191 , pp. 3257-3270
    • Marin, L.1    Lesnic, D.2
  • 19
    • 33748745580 scopus 로고    scopus 로고
    • L.C. Tartar, An introduction to Sobolev spaces and interpolation spaces, Lecture Notes, 2000. (〈http://www.math.cmu.edu/cna/pubblications.html〉).
  • 20
    • 0032164994 scopus 로고    scopus 로고
    • A nonlinear elliptic boundary value problem related to corrosion modeling
    • Vogelius M., and Xu J.-M. A nonlinear elliptic boundary value problem related to corrosion modeling. Quart. Appl. Math. 56 (1998) 479-505
    • (1998) Quart. Appl. Math. , vol.56 , pp. 479-505
    • Vogelius, M.1    Xu, J.-M.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.