[Turkmath:5924] (no subject)

[Allaberen Ashyralyev]

Dear Colleagues!

You are cordially invited to the  Weekly Online  Seminar “Analysis and
Applied Mathematics” on

Date: Tuesday, December 27, 2022

Time: 17.00-18.00 (Istanbul) = 15.00-16.00 (Ghent) = 20.00-21.00 (Almaty)

Zoom link:
https://us02web.zoom.us/j/6678270445?pwd=SFNmQUIvT0tRaH-lDaVYrN3l5bzJVQT09,
Conference ID: 667 827 0445, Access code: 1

Speaker: Prof. Dr. Michael V. Klibanov
University of North Carolina at Charlotte, USA

  Title:  Carleman Weighted Hilbert Spaces for Coefficient Inverse Problems
Abstract:Coefficient Inverse Problems (CIPs) are both ill-posed and highly
nonlinear. These two factors cause the non-convexity of conventional least
squares cost functionals, which are constructed for numerical solutions of
CIPs. The speaker with coauthors has developed a new approach to numerical
solutions of CIPs, called convexification. The convexification constructs
globally strictly convex cost functionals for a broad class of CIPs. This
functional is defined on a bounded convex set of an arbitrary but fixed
diameter in an appropriate Hilbert space, which we call Carleman Weighted
Hilbert Space. The weight is the Carleman Weight Function, which is used in
the Carleman estimate for a corresponding PDE operator. Uniqueness and
existence of the minimizer of such a functional on that set is established.
Convergence of minimizers to the true solution of the CIP is proven,
provided that the noise in the data tends to zero. Many numerical examples,
including ones with experimentally collected data, confirm the theory. Some
of these results will be presented in my talk. Main contributors are (in
the alphabetical order): Vo Khoa, Thuy Le and Loc Nguyen.
Abstracts and forthcoming talks can be found on our webpage
https://sites.google.com/view/aam-seminars
With my best wishes
*Prof. Dr. Allaberen Ashyralyev *
*Department of Mathematics, Bahcesehir University, 34353, Istanbul, Turkey*
*  and **Near East University, Lefkoşa(Nicosia), Mersin 10 Turkey*
*Peoples' Friendship University of Russia (RUDN University),** Ul Miklukho
Maklaya 6, Moscow 117198, Russian Federation *
*Institute of Mathematics and Mathematical Modelling, 050010, Almaty,
Kazakhstan*
*e-mail: allaberen.ashyralyev at eng.bau.edu.tr
<allaberen.ashyralyev at neu.edu.tr> and **aallaberen at gmail.com
<aallaberen at gmail.com> *
 http://akademik.bahcesehir.edu.tr/web/allaberenashyralyev

https://sites.google.com/view/aam-seminars
https://content.sciendo.com/view/journals/ejaam/ejaam-overview.xml
*icaam-online.org <http://icaam-online.org>*

*https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1
<https://www.genealogy.math.ndsu.nodak.edu/id.php?id=95872&fChrono=1>*
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