by Yevgeni SIROTININ, Dr. Sc. (Phys. & Math.), D. V. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University

Sergei Sobolev graduated in 1929 from what was then called Leningrad University. He got a job at the Theoretical Studies Department of the Institute of Seismology of the USSR Academy of Sciences where he worked under the guidance of a prominent Russian mathematician Prof. Vladimir Smirnov (Academician since 1943). He carried out a series of remarkable studies and published more than 40 scientific articles.

From 1932 Dr. Sobolev was on the staff of the Institute of Mathematics (from 1934- Institute of Mathematics named after V Steklov) of the USSR Academy of Sciences (Leningrad). In 1933 he was elected Corresponding Member of the Academy. After the Institute was moved to Moscow in 1934, he was appointed head of the Department of Differential and

Pages. 76

Functional Equations and Mathematical Physics. In 1935 he became professor of the Chair of Differential Equations of Moscow State University while continuing to lecture at his alma mater.

While continuing his intense scholarly activities, Prof. Sobolev passed on from dynamic problems of the theory of elasticity to statical problems: he focused on what are called border problems for elliptical equations of higher orders using direct methods of variation calculations. For polyharmonic equation the scholar applied new formulations of the prime numbers of the Dirichlet's theorem (German mathematician and foreign Corresponding Member of the St. Petersburg Academy of Sciences) in a range containing a multitude of different dimensions. This brought the scientist to a discovery of exceptional importance - the formulation of Sobolev's theorems. And in 1939 he was elected full Member of the USSR Academy of Sciences.

From 1939 to 1941 Prof. Sobolev held the post of deputy director of the Mathematics Institute of the USSR Academy of Sciences. In 1941 he became its director. In the difficult conditions of evacuation of the Institute to Kazan during the Great Patriotic War with Hitler Germany Prof. Sobolev did all he could to organize applied studies and to render effective support to the Soviet troops. Upon his return to Moscow in 1943 he got a job at the Laboratory No. 2 of the USSR Academy (today-Russian Research Center "Kurchatovsky Institute"). As the first deputy of Acad. Igor Kurchatov he was dealing with the problem of gas-diffusion enrichment of uranium. His name was mentioned in the resolution of February 11, 1946 of the Technical Council of the Special Committee of the USSR Sovnarkom (top governing body at the time) which discussed problems of mathematical support of Soviet atom bombs projects. In 1946 he was appointed, together with Acad. Isaac Kikoin and Corresponding Member of the Academy (from 1939) Ivan Voznesensky, scientific director of the project for the development of gas-diffusion methods of production of highly enriched U-235 for nuclear weapons. He was personally in charge of theoretical calculations of stable performance of the related equipment at Kombinat No. 813 (now - Uralsky Electrochemical Combine, Novouralsk, Sverdlovsk Region). Studies conducted by Acad. Sobolev accentuated the importance of developing new branches of Soviet industry - a program which called for designing and manufacturing of special equipment, including vacuum equipment. In doing that it was necessary to take into account that the uranium-containing gas (UF ₆ ) used in the new machinery was very aggressive chemically.

And Acad. Sobolev and members of his team worked out a necessary system of automatic regulation of the machinery and equipment cascades at the aforesaid plant. It involved thousands of pieces of machinery with tens of thousands of joints and connections and the launching of this system was a truly backbreaking job. To begin with, the new equipment could not match the stress of operation with the aggressive gas (of several thousand cubic meters in volume) and it was therefore necessary to design and build new units. It was only by the end of 1949 that the specialists understood the

Pages. 77

causes of the equipment failures and found ways of dealing with them. After that the plant called Combine No. 813 began producing uranium with 75 percent enrichment with U ²³⁵ isotope. Additional enrichment up to the weapons' grade was done with the help of an electromagnetic separator. The 90 percent level of enrichment was attained by 1951. These achievements of our scientists were used not only at the aforesaid Combine, but also at sister plants belonging to the system of what was called the First Directorate of the USSR Sovmin which was charged with the production of enriched uranium.

And it should be pointed out that a large share of Acad. Sobolev's activities in this field were associated with mathematical physics equations and it took him a lot of work and ingenuity in order to attain the needed results. It was necessary to comprehend the related physical process as a whole and to cope with some purely applied mathematical problems by using some very scarce computing equipment. It was necessary to calculate, optimize and predict some very complicated processes which had never been tackled before. Thanks to his extraordinary intuition and zeal Acad. Sobolev managed to cope with all of these specific problems exactly on time.

By a decision of the USSR Council of Ministers of June 10, 1948 Acad. Sobolev was put in charge of what was called Special Seminar at Laboratory No. 2 of the USSR Academy. Its objective consisted in the coordination of theoretical and practical studies, and control of the implementation of the program of development of nuclear weapons charges (RDS-1, RDS-2, RDS-3, RDS-4 and RDS-5, from 1949 to 1953)* and studies for the development of thermonuclear weapons.

From 1952 to 1959 Acad. Sobolev headed this country's first Chair of Computation Mathematics of the Moscow University Department of Mechanics and Mathematics. And although it had been set up back in 1949, it was Acad. Sobolev who laid the foundations of its ideological, research and pedagogical activities. At the same time he also lectured on equations with partial derivatives and conducted seminars. And from 1935 to 1958 (with a break only during the Great Patriotic War with Nazi Germany) he conducted one more seminar together with Acad. Ivan Petrovsky (since 1946) and Acad. Andrei Tikhonov (since 1966). This was a seminar on equations with partial derivatives which was the focal point of practically all studies in this area of mathematics conducted in Moscow and other research centers of this country.

1958 saw the start of what can be called the Novosibirsk period in the scientist's career. After the establishment of the Siberian Branch of the USSR Academy of Sciences he was appointed Director of the Institute of Mathematics (now bearing his name). And he saw to it that all key areas of modern research be put on its agenda. For example, the scientist himself never dealt with cybernetics and mathematical economics, but he did his best for the development of such studies at his Institute.

The main efforts of Acad. Sobolev were focused on the dynamics of elastic body. He was the first to build a general theory of plane (planar) waves in

* See: Ye. Sirotinin, "His Line: Physics of the Explosion", Science in Russia, No. 2, 2004. - Ed.

Pages. 78

resilient semispace* with a tension-free border and he also formulated the general concept of the surface wave. His studies provided a fundamental contribution to the theory of equations with partial derivatives, mathematical physics, theory of functions and functional analysis, computing mathematics, theory of elasticity and a number of areas of applied mathematics. The scholar enriched science with new ideas and concepts, laid the foundations of important theories and fields in mathematics; induced the concepts of generalized derivative and generalized solution of differential equation. He was one of the first to apply the ideas and methods of functional analysis to problems for equations with partial derivatives and to concrete problems of mathematical physics. His theory of functional spaces and theory of embedding provide the foundation of the modern methods of studies of equations with partial derivatives.

All of the works of Acad. Sobolev received a high assessment on the part of the Soviet government. His studies on the production of highly enriched U-235 brought him in 1951 the title of Hero of Socialist Labor and the second Stalin Prize award (first - in 1941). His subsequent contributions to the development of the Soviet atomic industry and mathematical science were honored with two State Prizes (1953 and 1986) and several orders.

The scientific activities of Acad. S. Sobolev received broad international recognition. He was elected Honorary Doctor of Humboldt University (Berlin), Honorary Doctor of Karlov University (Prague), Honorary Doctor of the Higher School of Architecture and Building Construction (Weimar, Germany), Foreign Member of the French Academy of Sciences, Foreign Member of the National Academy of dei Lyncei in Rome and Honorary Member of the Edinburgh Royal Society and of the American Mathematical Society.

* Semispace - multitude of points of space located on one side of a certain plane. - Ed.

Permanent link to this publication: