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An alternating boundary integral based method for a Cauchy problem for the Laplace equation in semi-infinite regions
1. | Faculty of Applied Mathematics and Computer Science, Ivan Franko National University of Lviv, 79000 Lviv, Ukraine |
2. | School of Mathematics, University of Birmingham, Edgbaston, Birmingham B15 2TT, United Kingdom |
References:
[1] |
G. Bastay, T. Johansson, V. A. Kozlov and D. Lesnic, An alternating method for the stationary Stokes system,, ZAMM, 86 (2006), 268.
doi: 10.1002/zamm.200410238. |
[2] |
J. Baumeister and A. Leitāo, On iterative methods for solving ill-posed problems modeled by partial differential equations,, J. Inv. Ill-Posed Probl., 9 (2001), 13.
|
[3] |
A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations,, Amer. J. Math., 80 (1958), 16.
doi: 10.2307/2372819. |
[4] |
T. Carleman, Sur un probléme d'unicité pur les systémes d'équations aux dérivées partielles á deux variables indépendantes, (French), Ark. Mat., 26 (1939), 1.
|
[5] |
R. Chapko and R. Kress, On a quadrature method for a logarithmic integral equation of the first kind, in "World Scientific Series in Applicable Analysis, Contributions in Numerical Mathematics,, Vol. 2'' (ed. Agarwal), 2 (1993), 127.
|
[6] |
H. W. Engl and A. Leitāo, A Mann iterative regularization method for elliptic Cauchy problems,, Numer. Funct. Anal. Optim., 22 (2001), 861.
doi: 10.1081/NFA-100108313. |
[7] |
U. Hämarik and T. Raus, On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data,, J. Inverse Ill-Posed Probl., 14 (2006), 251.
doi: 10.1515/156939406777340928. |
[8] |
M. A. Jawson and G. Symm, "Integral Equations Methods in Potential Theory and Elastostatics,'', Academic Press, (1977).
|
[9] |
M. Jourhmane and A. Nachaoui, An alternating method for an inverse Cauchy problem,, Numer. Algorithms, 21 (1999), 247.
doi: 10.1023/A:1019134102565. |
[10] |
V. A. Kozlov and V. G. Maz'ya, On iterative procedures for solving ill-posed boundary value problems that preserve differential equations,, Algebra i Analiz, 1 (1989), 144. Google Scholar |
[11] |
V. A. Kozlov, V. G. Maz'ya and A. V. Fomin, An iterative method for solving the Cauchy problem for elliptic equations,, Zh. Vychisl. Mat. i Mat. Fiz., 31 (1991), 64.
|
[12] |
R. Kress, "Linear Integral Equations,", 2nd edition, (1999).
|
[13] |
D. Lesnic, L. Elliot and D. B. Ingham, An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation,, Eng. Anal. Bound. Elem., 20 (1997), 123.
doi: 10.1016/S0955-7997(97)00056-8. |
[14] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,'', Cambridge University Press, (2000).
|
[15] |
D. Maxwell, M. Truffer, S. Avdonin and M. Stuefer, Determining glacier velocities and stresses with inverse methods: an iterative scheme,, to appear in Journal of Glaciology., (). Google Scholar |
[16] |
C. Miranda, "Partial Differential Equations of Elliptic Type,'', Springer-Verlag, (1970).
|
[17] |
A. Polyanin, "Handbook of Linear Partial Differential Equations for Engineers and Scientists,'', Chapman & Hall/CRC Press, (2002).
|
[18] |
F. Stenger, "Numerical Methods Based on Sinc and Analytic Functions,'', Springer-Verlag, (1993).
|
[19] |
G. M. Vainikko and A. Y. Veretennikov, "Iteration Procedures in Ill-Posed Problems,'', Nauka Publ., (1986).
|
show all references
References:
[1] |
G. Bastay, T. Johansson, V. A. Kozlov and D. Lesnic, An alternating method for the stationary Stokes system,, ZAMM, 86 (2006), 268.
doi: 10.1002/zamm.200410238. |
[2] |
J. Baumeister and A. Leitāo, On iterative methods for solving ill-posed problems modeled by partial differential equations,, J. Inv. Ill-Posed Probl., 9 (2001), 13.
|
[3] |
A.-P. Calderón, Uniqueness in the Cauchy problem for partial differential equations,, Amer. J. Math., 80 (1958), 16.
doi: 10.2307/2372819. |
[4] |
T. Carleman, Sur un probléme d'unicité pur les systémes d'équations aux dérivées partielles á deux variables indépendantes, (French), Ark. Mat., 26 (1939), 1.
|
[5] |
R. Chapko and R. Kress, On a quadrature method for a logarithmic integral equation of the first kind, in "World Scientific Series in Applicable Analysis, Contributions in Numerical Mathematics,, Vol. 2'' (ed. Agarwal), 2 (1993), 127.
|
[6] |
H. W. Engl and A. Leitāo, A Mann iterative regularization method for elliptic Cauchy problems,, Numer. Funct. Anal. Optim., 22 (2001), 861.
doi: 10.1081/NFA-100108313. |
[7] |
U. Hämarik and T. Raus, On the choice of the regularization parameter in ill-posed problems with approximately given noise level of data,, J. Inverse Ill-Posed Probl., 14 (2006), 251.
doi: 10.1515/156939406777340928. |
[8] |
M. A. Jawson and G. Symm, "Integral Equations Methods in Potential Theory and Elastostatics,'', Academic Press, (1977).
|
[9] |
M. Jourhmane and A. Nachaoui, An alternating method for an inverse Cauchy problem,, Numer. Algorithms, 21 (1999), 247.
doi: 10.1023/A:1019134102565. |
[10] |
V. A. Kozlov and V. G. Maz'ya, On iterative procedures for solving ill-posed boundary value problems that preserve differential equations,, Algebra i Analiz, 1 (1989), 144. Google Scholar |
[11] |
V. A. Kozlov, V. G. Maz'ya and A. V. Fomin, An iterative method for solving the Cauchy problem for elliptic equations,, Zh. Vychisl. Mat. i Mat. Fiz., 31 (1991), 64.
|
[12] |
R. Kress, "Linear Integral Equations,", 2nd edition, (1999).
|
[13] |
D. Lesnic, L. Elliot and D. B. Ingham, An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation,, Eng. Anal. Bound. Elem., 20 (1997), 123.
doi: 10.1016/S0955-7997(97)00056-8. |
[14] |
W. McLean, "Strongly Elliptic Systems and Boundary Integral Equations,'', Cambridge University Press, (2000).
|
[15] |
D. Maxwell, M. Truffer, S. Avdonin and M. Stuefer, Determining glacier velocities and stresses with inverse methods: an iterative scheme,, to appear in Journal of Glaciology., (). Google Scholar |
[16] |
C. Miranda, "Partial Differential Equations of Elliptic Type,'', Springer-Verlag, (1970).
|
[17] |
A. Polyanin, "Handbook of Linear Partial Differential Equations for Engineers and Scientists,'', Chapman & Hall/CRC Press, (2002).
|
[18] |
F. Stenger, "Numerical Methods Based on Sinc and Analytic Functions,'', Springer-Verlag, (1993).
|
[19] |
G. M. Vainikko and A. Y. Veretennikov, "Iteration Procedures in Ill-Posed Problems,'', Nauka Publ., (1986).
|
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