56 citations · 510 across the 96 of their papers we have counts for
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Nanostructures imaging via numerical solution of a 3-d inverse scattering problem without the phase information
Michael V. Klibanov, Loc H. Nguyen, Kejia Pan
Inverse scattering problems without the phase information arise in imaging of nanostructures whose sizes are hundreds of nanometers as well as in imaging of biological cells. The g…
On a problem of S.L. Sobolev
Michael V. Klibanov
In 1930 Sergey L. Sobolev [7,8] has proposed a construction of the solution of the Cauchy problem for the hyperbolic equation of the second order with variable coefficients in 3-d.…
Two reconstruction procedures for a 3-d phaseless inverse scattering problem for the generalized Helmholtz equation
Michael V. Klibanov, Vladimir G. Romanov
The 3-d inverse scattering problem of the reconstruction of the unknown dielectric permittivity in the generalized Helmholtz equation is considered. The main difference with the co…
Reconstruction procedures for two inverse scattering problems without the phase information
Michael V. Klibanov, Vladimir G. Romanov
This is a continuation of two recent publications of the authors about reconstruction procedures for 3-d phaseless inverse scattering problems. The main novelty of this paper is th…
Profitable forecast of prices of stock options on real market data via the solution of an ill-posed problem for the Black-Scholes equation
Michael V. Klibanov, Andrey V. Kuzhuget
A new mathematical model for the Black-Scholes equation is proposed to forecast option prices. This model includes new interval for the price of the underlying stock as well as new…
Numerical studies of an adaptive finite element method applied to the reconstruction of shapes of buried objects from experimental data
Larisa Beilina, Nguyen Trung Thành, Michael V. Klibanov +1
We perform extended studies of an adaptive finite element method applied to the reconstruction of shapes of buried objects from experimental backscattering data. We use experimenta…