ILIA VEKUA'S CENTENARY

The outstanding mathematician and mechanist Ilia Vekua was born on April 23, 1907 in Abkhazian village Shesheleti (West Georgia). After finishing a secondary school in the WestGeorgian town Zugdidi in 1925, he moved to Tbilisi, the capital of Georgia, where he entered the faculty of physics and mathematics of Tbilisi State University. He graduated the university with honors in 1930 and, following the recommendation of Academician Niko Muskhelishvili, left Tbilisi for Leningrad (now Sankt Petersburg) to continue his education there as a postgraduate student at the USSR Academy of Sciences. His initial research was conducted under the supervision of the well-known mathematician A. N. Krylov. In Leningrad Ilia Vekua published papers on problems of torsion and bending of elastic bars. He also worked on the theory of propagation of electric waves in an infinite layer with parallel plane boundaries and obtained the results which subsequently formed the basis of his thesis for the Candidate of Science degree.

After finishing the postgraduate course in 1933, Ilia Vekua returned to Tbilisi to work at his alma mater. He wholly devoted himself to scientific, educational and organizational activities. Ilia Vekua became an active participant in the famous seminar guided by Niko Muskhelishvili. He delivered lectures on mathematical physics, calculus of variations, differential and integral equations and was one of the founders of the Mathematical Institute of the Georgian Branch of the USSR Academy of Sciences (now A. Razmadze Mathematical Institute).

In 1951, Ilia Vekua moved to Moscow where he was officially invited for permanent residence and work. Together with his outstanding colleagues and friends M. A. Lavrent'ev, I. G. Petrovskii, and S. L. Sobolev, he directed the research seminars at V. A. Steklov Mathematical Institute and M. V. Lomonosov Moscow University.

Ilia Vekua was the founding rector (1959-1964) of Novosibirsk University. When living in Siberia, Ilia Vekua simultaneously combined several duties: he headed the theoretical department at the Hydrodynamics Institute of the Siberian Branch of the USSR Academy of Sciences, the mathematical physics chair of Novosibirsk University, and supervised the work of several scientific seminars.

After the USSR National Committee on Theoretical and Applied Mechanics was formed in 1956, Ilia Vekua became its permanent member. From 1963 he was member of the National Committee of Soviet Mathematicians.

At the end of 1964 Ilia Vekua returned to Tbilisi, where he was elected vice-president of the Georgian Academy of Sciences (1964-1965) and head of the higher mathematics chair at Tbilisi State University (1966-1972). On his initiative and under his guidance the department of mechanics was organized (1964) at A. Razmadze Mathematical Institute, and the problem laboratory of applied mathematics was founded (1966) at Tbilisi State University, which shortly was reorganized into the Institute of Applied Mathematics (1968). The latter institute is named after Ilia Vekua as he was its founder and remained its director and scientific leader (1968-1977) till the last days of his life. Throughout 1972-1977, Ilia Vekua was the president of the Georgian Academy of Sciences.

Ilia Vekua's research works cover various fields of mathematics and mechanics. Many of them are devoted to the theory of partial differential equations in which Ilia Vekua took a great interest. In the analytical theory of linear differential equations of elliptic type with two independent variables, an important part was played by formulas of general representation of solutions by means of analytic functions of one complex variable. These formulas made it possible to widen considerably the field of application of the methods of the classical theory of analytic functions of a complex variable. Based on these studies, Ilia Vekua developed new methods for solving boundary value problems which enabled him to investigate a vast class of boundary value problems formulated in nonclassical sense. The method he proposed for reducing boundary value problems to singular integral equations is one of the most powerful means for studies in this field. Special mention should be made of a general boundary value problem for elliptic equations, which Ilia Vekua formulated and studied most completely. The well known boundary value problems of Dirichlet, Neumann and Poincar'e are particular cases of this problem. Ilia Vekua derived the formulas of integral representation of holomorphic functions, which in the mathematical literature are named after him, and used them as an important tool in investigating the problem.

Ilia Vekua is one of the founders of the theory of generalized analytic functions.

Ilia Vekua worked out several versions of the mathematical theory of elastic shells.

In spite of his grave illness, Ilia Vekua continued to pursue his scientific, teaching and organizational activities till the last days of his life. His last monographs were published posthumously. In September 1976, at Ilia Vekua's suggestion, the IUTAM's General Assembly decided to organize the 3rd International Symposium on the Theory of Shells in Tbilisi, Georgia. Ilia Vekua was appointed chairman both of the international scientific committee and of the national organizing committee. Preparations for the symposium were underway when the whole scientific world was deeply saddened by the untimely demise of Ilia Vekua on December 2, 1977. The symposium which the IUTAM held in Tbilisi in August 22-28, 1978, was dedicated to his memory.

R.P. Gilbert, G.V. Jaiani

Newark, October, 2007