# Alemdar Hasanoglu

Alemdar Hasanov Hasanoğlu *)

Prof. Alemdar Hasanov Hasanoğlu is a Soviet - Azerbaijani mathematician, distinguished scholar in the inverse problems community and a well-known expert in the field of inverse problems and mathematical modeling. He was born in 1954 in the Gazakh district of Azerbaijan, former USSR. His mother Vezire was a teacher and his father Ibrahim was a school director, who was later appointed as the Head of the Education Department of the Gazakh district, Azerbaijan USSR.

Being graduated from high school with honors in June 1971, he had twice won prizes at the Azerbaijan National Mathematical Olympiad in 1969 and 1971 during his school years. In 1971 he became a student at the Mathematics and Mechanics Faculty of Baku State University (BSU) Azerbaijan which was one of the top research universities in the USSR, especially in the areas of functional analysis and differential equations. Also in 1974, he won the nationwide round of the University Olympiad and was elected a participant of the First Soviet Student Olympiad, organized at Moscow State University by one of the twentieth century's greatest mathematicians Andrey Nikolaevich Kolmogorov. He graduated from BSU with honors in June 1976 and earned his Master of Science degree in Mathematics.

Alemdar began his scientific career as a researcher (1977-1979) at the Keldysh Institute of applied mathematics USSR Academy of Sciences, in Department No 3, chaired by Aleksander A. Samarskii, a prominent Soviet-Russian mathematician and a supreme authority in computational mathematics and mathematical modeling in USSR. In 1979, Alemdar became a Ph.D. student at the Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University, founded in 1970 by Andrey Tikhonov, a Soviet- Russian mathematician known for important contributions functional analysis, mathematical physics, and ill-posed problems. Working on his doctoral dissertation under the scientific supervision of professors Aleksander A.Samarskii and Vladimir B. Andreev in the department of Mathematical Physics, Alemdar Hasanov focused on a challenging and important problem, formulated by Jacques-Louis Lions in his famous book Quelques Méthodes de Résolution des Problèmes aux Limites non Linéaires (Paris, Dunod, 1969), for elliptic variational inequalities (EVI). It is known that the main distinguishing feature of the EVI corresponding to a positive defined elliptic operator, is that a part of the boundary of the domain, is also unknown, and needs to be defined. If this part could be found by any way, then the EVI could be transformed into the integral identity. Analyzing unilateral boundary conditions, Lions pointed out that the most important problem here is the study of the behavior of the solution of EVI on perturbed boundaries. In these basic directions Alemdar has obtained fundamental results [1-3]. These theoretical results have not only the precise physical meaning applied to Signorini type problems, i.e. boundary value problems with unilateral constraints, but also permit one to construct locally adaptable mesh algorithm for these problems. The first series of these results have been published in the journal Differential Equations [1-2]. Further results including an approximation of variational inequalities in an infinite-dimensional space, has been then published in Doklady Mathematics [3].

Alemdar Hasanov received his Ph.D. in Computational Mathematics from Moscow State University in September 1982. In October 1982 he received the position of Assistant Professor in the Department of Computational Mathematics Baku State University, where he worked there until 1986. From 1986 to 1988, Alemdar joined again the Faculty of Computational Mathematics and Cybernetics, Moscow State University, to complete a dissertation leading to Doctor of Science degree in Physics and Mathematics. During this period he was a chair of various scientific- technological projects related to mathematical modeling, computational methods and nonlinear equations, in addition to his professional work in university. These projects were supported by such well-recognized leading organizations as All Union Physico-Technical and Radio- Technical Measurement Institute (Solnechnogorsk, Moscow Region), Institute of Machines Science named after A.A. Blagonravov of the USSR Academy of Sciences (Moscow), and the Scientific-Technological Union “Technology” (Obninsk, Moscow Region). These institutions were leading scientific organizations to focus on a high priority military technology. One of main scientific and technological problems in these projects was related to the identification unknown elasto-plastic properties of materials based on experimental data obtained during spherical indentation testing. Note that the spherical indentation testing was, and still is, one of extensively used experimental methods to measure the hardness of metal and polymer materials. The objective here is usually to analyze the indentation curve as dependent on the size of the sample (indent) and indenter relative to the material length parameters, strain hardening, and yield stress to modulus ratio. From an engineer’s viewpoint, the problem of determining real elastoplastic properties, based on the measured indentation curve, obtained experimentally during the uniaxial quasi-static indentation process, was one of extremely significant and important problems in material science and technology. In engineering terms of that period, this problem has been defined as the nondestructive diagnostics of an elastoplatic medium. On the other hand, it is known that within the framework of the deformation theory of plasticity, these properties can be described by following stress-strain relationship. It inspired Alemdar to create a mathematical model of the nondestructive diagnostics problem. The first pioneering results related to the nondestructive diagnostics problem for an elastoplatic medium have been obtained in 1986 [4]. Alemdar formulated this problem as a coefficient identification problem for 3D nonlinear Lame equations, with an integral overdetermination. Then he used the quasi-solution approach with Tikhonov regularization, to prove an existence of a solution of the inverse problem.

These results have been discussed in the Seminar of the well-known expert in inverse problems, Professor Vladimir A. Morozov, the author of the concept “Morozov's discrepancy principle”, at the Research Computing Center of Lomonosov Moscow State University, in May, 1987. With helpful suggestions of Professor Morozov, some results has then been presented by Academician A.A. Samarskii to the journal Doklady Mathematics [5]. At that time, Alemdar did not know much about coefficient inverse problems (CIPs), in particular about pioneering works of J. Cannon and P. DuChateau on parabolic CIPs, due to the difficulties of accessing foreign scientific journals in former USSR. After relocating to Turkey in 1992, he was truly surprised to find out that his result in [5] was actually a first attempt to solve a CIP for nonlinear equation, when a measured data is given in integral form (defined now as non-local measured output). Only thirty years later, mathematicians and engineers began to discuss an ill-posedness of this problem (see, for example, [L. Liu, N. Ogasawara, N. Chiba, X. Chen, Can indentation test measure unique elastoplastic properties, Journal of Materials Research, 24 (2009) 784- 800]).

In February 1988 Alemdar completed his dissertation and in October 1988 the Special Scientific Committee chaired by Academician Andrey N. Tikhonov at the Moscow State University conferred upon him the highest scientific degree - Doctor of Science in Physics and Mathematics on “Mathematical Modelling, Methods and Computational Technologies in Science”. He was youngest to receive this degree in this area in all of the Soviet Union. A year later he was awarded the Medal of USSR Academy of Sciences at the Exhibition of Achievements of USSR National Economy, on “Fundamental Sciences in Technology” (Cert. No 480-N, 02.08.89), for the series of scientific works “Computational Express-Nondestructive Diagnostics of Engineering Materials”. Five years later this work has been published in SIAM Journal of Applied Mathematics [6]. This is one of the pioneering works on coefficient inverse problems for nonlinear PDEs. In 1989 he became Full Professor at the Baku State University, Azerbaijan.

In 1992 the Scientific and Technological Research Council of Turkey invited Alemdar Hasanov to Marmara Research Center. A year later he was invited to Kocaeli University, to organize a new Applied Mathematical Sciences Research Center. In October 1996 he was invitated by the Department of Mathematics University of Nebraska as a Visiting Research Professor position, for the Spring Semeter 1997. During this period Alemdar worked with Steve Cohn on identification problems for nonlinear parabolic equations arising in electrochemistry, with Jennifer Mueller on backward problems, and with Paul DuChateau on coefficient inverse problems.

He kept his position as the director of the Applied Mathematical Sciences Research Center at Kocaeli University until 2009, when he gets an invitation from the new organized Izmir University. He invited the best mathematicians from the former Soviet Union and organized one of the best research centers which had scientific contacts with the world’s leading centers. Alemdar extended here his research of direct and inverse problems in nonlinear mechanics to inverse problems for a nonlinear bending plate [7] and inverse coefficient problems for elliptic variational inequalities with a nonlinear monotone operator [8-11]. In addition to the above mentioned problems, Alemdar became interested in inverse source problems for evolution equations. He made essential contributions developing the systematic use of functional analysis and weak solution approach for solving these problems, both theoretically and numerically.Some of these results are given in [12-14]. Developing these results proposed a unique integral representation formula for unique regularized solution of inverse source, as well as backward problems with final over-determination for evolution equations [15-16]. Then he proved that, in the constant coefficient linear parabolic and hyperbolic equations cases, this representation formula is an integral analogue of well-known Picard’s Singular Value ecomposition for compact (i.e. input-output) operators

During the years of work as the Head of the research Center, he organizoval new programs for graduates and doctoral students. Due to these programs, he has many excellent PhD and post-doctoral students from Turkey and outside. Thanks to his productive work, he was able to not only conduct extensive scientific research, but also complete his well- recognized books Variational Problems and Finite Element Method, Literatur, Istanbul (2001); Partial Differential Equations,Literatur,Istanbul(2010). Contributions of this Research Center to the development of applied mathematics in Turkey are reported in various official documents, in particular, in the Scientific Report on the 75th Anniversary of the Republic of Turkey, published as a book by the Turkish Academy of Sciences [Science in the 75th Year of the Turkish Republic 1923-1998, Turkish Academy of Sciences (TUBA), Ankara, 1999, page 74-75].

The results of many years of work on inverse problems, as well as actively working with Vladimir G. Romanov since 2012, are reflected in the book Introduction to Inverse Problems for Differential Equations, published by Springer in 2017, which is defined by Springer as the “First systematic and comprehensive introductory book on inverse problems for differential equations” (https://link.springer.com/book/10.1007/978-3-030-79427-9).

A series of works by Hasanov published in 2019-2021 on new classes of inverse problems related to dynamic damped Euler-Bernoulli and Kirchhoff-Love plate equations [17-18, 22-23], and inverse coefficient problems [19-21] for the damped wave equation, have a special place in theory and applications. Remark that although these problems have been studied since the 60th year of the last century, neither the role of the damping parameter, nor the “subdomains defined by characteristics”, was investigated in any of these studies. It should be emphasized that in contrast to the inverse problems for undamped wave equation

studied in unbounded domain, in an inverse problem related to the damped wave equation one needs, first of all, to take into account the damping factor, the presence of which changes the entire structure of the problem as well as its solution. Specifically, the damping factor leads to a number of characteristic features in the propagation of waves through the conductor and in reflection from conducting surfaces. The first consequence of these is the formation of various domains, called “*subdomains defined by characteristics*”, by the reflected wave from the boundary. It is precisely in these areas that all analyzes related to direct, adjoint and inverse problems should be carried out. This phenomenon has first been examined in detail in [20], and then in [21-22], for other inverse coeficient problems.

It is impossible to identify all works and contributions of Dr. Hasanov to applied mathematics, in particular, to inverse problems. Nevertheless, we need to underline two essential points. First, the spectrum of his contributions is very wide from applied mathematics, engineering sciences and medicine to computational methods. Second, almost all models and methods proposed by Dr. Hasanov are original and contain new ideas. As a result, he has published more than 100 articles in about 20 different mathematical, engineering and medical journals. His research projects has been supported by U.S.S.R Academy of Sciences institutions (1982-1989), Kocaeli Governorship, Arcelik A. S., Istanbul Municipality, TUBTAK , Turkey (1994-2018), Office of Naval Research, USA (2002), INTAS, Brussels (2007-2009), Science for Peace and Security Section, NATO, Brussels (2008-2010), Japan Society for the Promotion of Science (JSPS) (2018). He has supervised 16 PhD students in Turkey and outside. Most of these students students became his research collaborators. Dr. Hasanov been also an invited speaker at many important international conferences.

Alemdar Hasanov, Albert Tarantola, and Alex Tolstoy were the first initiators and organizers

of the First International Conference "Inverse Problems: Modeling and Simulation" (IPMS 2002, Fethiye, Turkey)

His has such an active and colorful life that we may only outline some aspects of it in the form of highlights. First of all, having a deep love to literature and arts, Dr. Hasanov is known as a person who has produced unique ideas both in philosophy and social sciences. He has been solidesity with young researchers studying in different countries around the world in all fields of life, including financial support. It is amazing to realize how many engineers, mathematicians, also different distinguished people with different professions from various countries, have been, and are still, collaborating with Alemdar. These people, as well as the related research subjects, are too numerous to be listed here.

Professor Hasanov is a founder of one of best international conference series on inverse problems,”Inverse Problems: Modeling and Simulation” (IPMS) (https://www.ipms- conference.org/ipms2022/), and also The Eurasian Association on Inverse Problems (EAIP) (https://www.eurasianip.org/). Since 2002, every 2 years, for more than 20 years, IPMS conference series has brought together many members of the inverse problems community, to discuss the latest scientific results on inverse problems and applications.

This photo shows the most famous representatives of the inverse problems community IPMS 2014, Fethiye, Turkey

All the IPMS meetings have become symbols for the inverse problems community and young scientists are bestowed with IPMS awards at these meeting for their excellent achievements. The series of special issues related to IPMS conferences are remarkable.

The EAIP Young Scientist Award Ceremony at the Ninth International Conference IPMS 2018

Malta Awardeers: Giovanni S. Alberti, University of Genoa, Italy, Andrei Shurup, Lomonosov Moscow State University, Russia

The EAIP Award Ceremony at the Ninth International Conference IPMS 2018

Malta Awardeer: Prof. Dr. Otmar Scherzer (University of Vienna)

It took Alemdar 5 years to finally give birth to the newly formed Eurasian Association on Inverse Problems (EAIP), which coordinates and supports international research activities of scientists in the Eurasian Plate and elsewhere (https://www.eurasianip.org/)The awards, EAIP Award and EAIP Young Scientist Award of The Eurasian Association on Inverse Problems association are currently one of the most distinguished international awards of this branch of science.

Alemdar with his wife Şafak and sons Aziz and Rahman

On behalf of his colleagues, students, and friends from all over the world, we would like to wish Alemdar every success in his scientific work and much happiness with his wife Şafak and his sons Aziz and Rahman, and also grandson Ayaz. For Alemdar, retirement is just a formality. In fact, he is more active now, both in science and in organizational matters. He is not an outstanding organizer of various international conferences and plays a leading role in the inverse problems community. He is also a very nice and friendly person.

REFERENCES

- A. I. Gasanov (Alemdar Hasanov), Numerical method for solving a contact problem of elasticitytheory in the absence of friction forces, Differentsialnye-Uravneniya [Differentsialnye- Uravneniya] 18(1982), 1156-1161. MR: 84g: 73052.
- A. I. Gasanov (Alemdar Hasanov), Properties of normal stresses and displacements near a perturbed boundary of the contact zone, Differentsialnye-Uravneniya [Differentsialnye-Uravneniya] 19 (1983), 1181-1186. MR: 85a: 73085.
- A. I. Gasanov (Alemdar Hasanov), Approximation of variational inequalities in an infinitedimensional space, Dokl.-Akad.-Nauk-SSSR 285 (1985), 20-23. MR: 86m: 49016.
- A. I. Gasanov (Alemdar Hasanov), An inverse problem for reconstruction of elastoplastic properties on the basis of an indentation diagram, Differentsialnye-Uravneniya [Diferentsialnye- Uravneniya] 22 (1986), no.7, 1260-1263, 1288. MR: 87k: 73020.
- A. I. Gasanov (Alemdar Hasanov), An inverse problem of nondestructive diagnostics of an elastoplatic medium, Dokl.-Akad.-Nauk-SSSR [Doklady-Akademii-Nauk-SSSR] 298 (1988), 1299- 1303. MR: 89c: 73029.
- Alemdar Hasanov, An inverse coefficient problem for an elasto-plastic medium, SIAM J. Appl. Math., 55(1995) 1736-1752.
- Alemdar Hasanov, Azer Mamedov, An inverse problem related to the determination of elastoplastic properties of a plate, Inverse Problems, 10(1994) 601-615.
- Alemdar Hasanov, Zahir Seyidmamedov, The solution of an axisymmetric inverse elasto- plastic problem using penetration diagram, International Journal of Non-Linear Mechanics, 30(1995) 465-477.
- Alemdar Hasanov, Inverse coefficient problems for monotone potential operators, Inverse Problems, 13(1997) 1265-1278.
- Alemdar Hasanov, Inverse coefficient problems for elliptic variational inequalities with a nonlinear monotone operator, Inverse Problems, 14(1998) 1151-1169.
- Alemdar Hasanov, Some new classes of inverse coeffcient problems in nonlinear mechanics and computational material science, Int. J. Non-Linear Mechanics, 46(2011) 667-684.
- Alemdar Hasanov, Simultaneous determination of source terms in a linear parabolic problem from the final overdetermination: weak solution approach, J. Math. Anal. Appl., 330(2007) 766-779.
- Alemdar Hasanov, Simultaneous determination of source terms in a linear hyperbolic problem from the final overdetermination: weak solution approach, IMA Appl. Math., 74(2009) 1-19.
- Alemdar Hasanov, Identification of unknown source term in a vibrating cantilevered beam from final overdeterminations, Inverse Problems, 25(2009) 115015 (19pp).
- Alemdar Hasanov, Burhan Pektaş, A unified approach to identifying an unknown spacewise dependent source in a variable coefficient parabolic equation from final and integral overdeterminations, Applied Numerical Mathematics, 78(2014) 49-67.
- Alemdar Hasanov, Balgaisha Mukanova, Relationship between representation formulas for unique regularized solutions of inverse source problems with final overdetermination and singular value decomposition of input-output operators, IMA J. Appl. Math., 74(2014) 1-19.
- Alemdar Hasanov, Onur Baysal and Cristiana Sebu, Identification of an unknown shear force in the Euler-Bernoulli cantilever beam from measured boundary defection, Inverse Problems, 35(5) (2019)
- Alemdar Hasanov amd Onur Baysal, Identification of a temporal load in a cantilever beam from measured boundary bending moment, Inverse Problems, 35(10) (2019)
- Vladimir Romanov and Alemdar Hasanov, Reconstruction of the principal coefficient in the damped wave equation from Dirichlet-to-Neumann operator, Inverse Problems, 36(2) (2020)
- Vladimir Romanov and Alemdar Hasanov, Recovering a potential in damped wave equation from Neumann-to-Dirichlet operator, Inverse Problems, 36(11) (2020)
- Vladimir Romanov and Alemdar Hasanov, Recovering a potential in damped wave equation from Dirichlet-to-Neumann operator, Inverse Problems 37(2021)
- Vladimir Romanov, Alemdar Hasanov and Onur Baysal, Unique recovery of unknown spatial load in damped Euler-Bernoulli beam equation from final time measured output, Inverse Problems 37 (2021).
- Anjuna Dileep, Kumarasamy Sakthivel and Alemdar Hasanov, Determination of a spatial load in a damped Kirchhoff-Love plate equation from final time measured data, Inverse Problems 37 (2021)

*) A reduced version of this article was published in

V.B. Andreev, H.T. Banks, G.S. Dulikravich, B. Hofmann, S.I. Kabanikhin, F.J. Kuchuk, D. Lesnic,

M. Z. Nashed, A. Neubauer, V.G. Romanov, M.Slodicka, V. V. Vasin, A.G. Yagola and F. Zirilli, In celebration of the 60th birthday of Professor Alemdar Hasanoglu (Hasanov), *Journal of Inverse and Ill-Posed Problems*, **24**(2) 2014; 109-110