56 citations · 510 across the 96 of their papers we have counts for
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Simultaneous Reconstructions of (x,t) -Dependent Coefficients and Initial Conditions of Parabolic Equations
Michael V. Klibanov
This is the first publication, in which an inverse problem of the simultaneous reconstruction of an unknown (x,t) - dependent coefficient and an unknown initial condition in a gene…
On an Dimensional Travel Time Tomography Problem
Michael V. Klibanov
In their seminal works Herglotz (1905) and Wiechert and Zoeppritz (1907) have solved the so-called Travel Time Tomography Problem (TTTP) in the 1-D case. However, the question abou…
A New Type of Ill-Posed and Inverse Problems for Parabolic Equations
Michael V. Klibanov
The time dependent experimental data are always collected at discrete grids with respect to the time t. The step size h of such a grid is always separated from zero by a certain po…
Lipschitz Stability Estimate and Uniqueness in the Retrospective Analysis for The Mean Field Games System via Two Carleman Estimates
Michael V. Klibanov, Yurii Averboukh
A retrospective analysis process for the mean field games system (MFGS) is considered. For the first time, Carleman estimates are applied to the analysis of the MFGS. Two new Carle…
Stability Estimates for Some Parabolic Inverse Problems With the Final Overdetermination via a New Carleman Estimate
Michael V. Klibanov
This paper is about Holder and Lipschitz stability estimates and uniqueness theorems for some coefficient inverse problems and associated inverse source problems for a general line…
Convexification for the inversion of a time dependent wave front in a heterogeneous medium
Michael V. Klibanov, Jingzhi Li, Wenlong Zhang
An inverse scattering problem for the 3D acoustic equation in time domain is considered. The unknown spatially distributed speed of sound is the subject of the solution of this pro…