[1]

G. S. Alberti, H. Ammari, B. Jin, J.-K. Seo and W. Zhang,
The linearized inverse problem in multifrequency electrical impedance tomography,
SIAM J. Imaging Sci. 9 (2016), no. 4, 1525–1551.
CrossrefWeb of ScienceGoogle Scholar

[2]

A. B. Bakushinskii, M. V. Klibanov and N. A. Koshev,
Carleman weight functions for a globally convergent numerical method for ill-posed Cauchy problems for some quasilinear PDEs,
Nonlinear Anal. Real World Appl. 34 (2017), 201–224.
Web of ScienceCrossrefGoogle Scholar

[3]

L. Beilina,
Energy estimates and numerical verification of the stabilized domain decomposition finite element/finite difference approach for time-dependent Maxwell’s system,
Cent. Eur. J. Math. 11 (2013), no. 4, 702–733.
Web of ScienceGoogle Scholar

[4]

L. Beilina and M. V. Klibanov,
Globally strongly convex cost functional for a coefficient inverse problem,
Nonlinear Anal. Real World Appl. 22 (2015), 272–288.
Web of ScienceCrossrefGoogle Scholar

[5]

M. I. Belishev,
Recent progress in the boundary control method,
Inverse Problems 23 (2007), no. 5, R1–R67.
CrossrefGoogle Scholar

[6]

M. I. Belishev, I. B. Ivanov, I. V. Kubyshkin and V. S. Semenov,
Numerical testing in determination of sound speed from a part of boundary by the BC-method,
J. Inverse Ill-Posed Probl. 24 (2016), no. 2, 159–180.
Web of ScienceGoogle Scholar

[7]

A. Friedman,
Partial Differential Equations of Parabolic Type,
Prentice-Hall, Englewood Cliffs, 1964.
Google Scholar

[8]

D. Gilbarg and N. S. Trudinger,
Elliptic Partial Differential Equations of Second Order, 2nd ed.,
Grundlehren Math. Wiss. 224,
Springer, Berlin, 1983.
Google Scholar

[9]

B. Harrach and M. N. Minh,
Enhancing residual-based techniques with shape reconstruction features in electrical impedance tomography,
Inverse Problems 32 (2016), no. 12, Article ID 125002.
Web of ScienceGoogle Scholar

[10]

N. Hyvönen, P. Piiroinen and O. Seiskari,
Point measurements for a Neumann-to-Dirichlet map and the Calderón problem in the plane,
SIAM J. Math. Anal. 44 (2012), no. 5, 3526–3536.
CrossrefGoogle Scholar

[11]

B. Jin, Y. Xu and J. Zou,
A convergent adaptive finite element method for electrical impedance tomography,
IMA J. Numer. Anal. 37 (2017), no. 3, 1520–1550.
Web of ScienceGoogle Scholar

[12]

S. I. Kabanikhin, K. K. Sabelfeld, N. S. Novikov and M. A. Shishlenin,
Numerical solution of the multidimensional Gelfand–Levitan equation,
J. Inverse Ill-Posed Probl. 23 (2015), no. 5, 439–450.
Web of ScienceGoogle Scholar

[13]

S. I. Kabanikhin, A. D. Satybaev and M. A. Shishlenin,
Direct Methods of Solving Multidimensional Inverse Hyperbolic Problems,
Inverse Ill-posed Probl. Ser.,
VSP, Utrecht, 2005.
Google Scholar

[14]

M. V. Klibanov,
Global convexity in a three-dimensional inverse acoustic problem,
SIAM J. Math. Anal. 28 (1997), no. 6, 1371–1388.
CrossrefGoogle Scholar

[15]

M. V. Klibanov,
Carleman estimates for global uniqueness, stability and numerical methods for coefficient inverse problems,
J. Inverse Ill-Posed Probl. 21 (2013), no. 4, 477–560.
Web of ScienceGoogle Scholar

[16]

M. V. Klibanov,
Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs,
Inverse Problems 31 (2015), no. 12, Article ID 125007.
Web of ScienceGoogle Scholar

[17]

M. V. Klibanov and V. G. Kamburg,
Globally strictly convex cost functional for an inverse parabolic problem,
Math. Methods Appl. Sci. 39 (2016), no. 4, 930–940.
Web of ScienceCrossrefGoogle Scholar

[18]

M. V. Klibanov and V. G. Romanov,
Reconstruction procedures for two inverse scattering problems without the phase information,
SIAM J. Appl. Math. 76 (2016), no. 1, 178–196.
Web of ScienceCrossrefGoogle Scholar

[19]

M. V. Klibanov and N. T. Thành,
Recovering dielectric constants of explosives via a globally strictly convex cost functional,
SIAM J. Appl. Math. 75 (2015), no. 2, 518–537.
Web of ScienceCrossrefGoogle Scholar

[20]

M. V. Klibanov and A. Timonov,
Carleman Estimates for Coefficient Inverse Problems and Numerical Applications,
Inverse Ill-posed Probl. Ser.,
VSP, Utrecht, 2004.
Google Scholar

[21]

O. A. Ladyženskaja, V. A. Solonnikov and N. N. Ural’ceva,
Linear and Quasilinear Equations of Parabolic Type,
Transl. Math. Monogr. 23,
American Mathematical Society, Providence, 1968.
Google Scholar

[22]

E. L. Lakshtanov, R. G. Novikov and B. R. Vainberg,
A global Riemann-Hilbert problem for two-dimensional inverse scattering at fixed energy,
Rend. Istit. Mat. Univ. Trieste 48 (2016), 21–47.
Google Scholar

[23]

M. M. Lavrentiev, A. V. Avdeev, M. M. Lavrentiev, Jr. and V. I. Priimenko,
Inverse Problems of Mathematical Physics,
Inverse Ill-posed Probl. Ser.,
VSP, Utrecht, 2003.
Google Scholar

[24]

A. I. Nachman,
Global uniqueness for a two-dimensional inverse boundary value problem,
Ann. of Math. (2) 143 (1996), no. 1, 71–96.
CrossrefGoogle Scholar

[25]

D.-L. Nguyen, M. V. Klibanov, L. H. Nguyen, A. E. Kolesov, M. A. Fiddy and H. Liu,
Numerical solution of a coefficient inverse problem with multi-frequency experimental raw data by a globally convergent algorithm,
J. Comput. Phys. 345 (2017), 17–32.
CrossrefWeb of ScienceGoogle Scholar

[26]

D.-L. Nguyen, L. H. Nguyen, M. V. Klibanov and M. A. Fiddy,
Imaging of buried objects from multi-frequency experimental data using a globally convergent inversion method,
preprint (2017), https://arxiv.org/abs/1705.01219;
to appear in J. Inverse Ill-Posed Probl.

[27]

R. G. Novikov,
A multidimensional inverse spectral problem for the equation $-\mathrm{\Delta}\psi +(v(x)-Eu(x))\psi =0$,
Funct. Anal. Appl. 22 (1988), no. 4, 263–272.
Google Scholar

[28]

R. G. Novikov and M. Santacesaria,
Monochromatic reconstruction algorithms for two-dimensional multi-channel inverse problems,
Int. Math. Res. Not. IMRN (2013), no. 6, 1205–1229.
Google Scholar

[29]

J. Sylvester and G. Uhlmann,
A uniqueness theorem for an inverse boundary value problem in electrical prospection,
Comm. Pure Appl. Math. 39 (1986), no. 1, 91–112.
CrossrefGoogle Scholar

## Comments (0)

General note:By using the comment function on degruyter.com you agree to our Privacy Statement. A respectful treatment of one another is important to us. Therefore we would like to draw your attention to our House Rules.