V.I.Romanovskiy Institute of Mathematics, Uzbekistan Academy of Sciences

Tokhtamurod Juraevich Juraev (1934-2009) - renowned mathematician, Doctor of Physical and Mathematical Sciences, Professor, Full Member of the Academy of Sciences of the Republic of Uzbekistan and Academician of Turkey's Atatürk International Academy of Culture and Knowledge, Academician of the International Academy of Science, Education, Industry and Arts (USA), Honored Scientist of Uzbekistan, laureate of the Beruni State Prize of the Republic.

T.J. Juraev was a major specialist who created a scientific school in the field of partial differential equations, an outstanding organizer of science and higher education in the republic, and a renowned scientist who made significant contributions to the development of mathematics. The establishment and rapid development of the world-renowned scientific school in the direction of mixed and mixed-composite type equations theory of mathematical research in Uzbekistan is directly connected with the name of T.J. Juraev.

T.J. Juraev's fundamental scientific research aimed at creating the theory of non-classical equations of mathematical physics, as well as his scientific works of both theoretical and practical significance devoted to solving mathematical problems of boundary layer theory, which are urgent problems of mechanics, were recognized by the world mathematical community and brought him among the world-renowned researchers in this field.

T.J. Juraev was born on October 25, 1934, in the Yangiyul district of Tashkent region. In 1953, after graduating from secondary school, he entered the mathematics department of the Faculty of Physics and Mathematics at Central Asian State University and graduated with honors in 1958. The future scientist's diploma thesis was recommended for publication in a scientific journal.

The world-renowned scientific schools led by mathematicians, particularly academicians A.V. Bisadze and O.A. Oleinik, had a great and fruitful influence on the formation of T.J. Juraev as a scientist. The talented scientist gained enormous scientific prestige through his arduous and productive work: he defended his candidate's dissertation in 1962 and his doctoral dissertation in 1972, and was awarded the title of professor in 1974. That same year, T.J. Juraev was awarded the Abu Rayhan Beruni State Prize for his research in differential equations theory. In 1979, he became a Corresponding Member of the Academy of Sciences of the Republic of Uzbekistan, and in 1991 was awarded the honorary title "Honored Scientist of Uzbekistan."

T.J. Juraev made significant contributions to developing the theory of boundary value problems for non-classical equations of mathematical physics. He systematically analyzed mixed elliptic-hyperbolic, elliptic-parabolic, and parabolic-hyperbolic equations, and his research on the latter two types of equations is considered the most important and forms the foundation of scientific investigations in this direction.

For the first time, T.J. Juraev posed and investigated boundary value problems for mixed parabolic-hyperbolic equations with unknown lines of type change, which are extremely important for practical applications. Today, this direction is being rapidly developed by his students under the name "problems with unknown boundaries." The study of parabolic-hyperbolic equations in three-dimensional finite and infinite domains was first initiated in the works of T.J. Juraev and his students.

The study of higher-order partial differential equations occupies a large place in T.J. Juraev's research. He showed methods for complete classification and canonical representation of third and fourth-order equations. Under the direct supervision of T.J. Juraev, for the first time, higher odd-order equations with multiple characteristics were analyzed, their fundamental and elementary solutions were constructed, and the properties and characteristics of these solutions were studied and applied to solving boundary value problems.

Tokhtamurod Juraevich's scientific works devoted to posing and studying boundary value problems for third-order equations containing elliptic-parabolic and elliptic-hyperbolic operators in the principal part are considered the foundation of fundamental works in the theory of mixed-composite type equations. Here, a new method for solving equations was proposed, namely the method of reducing composite and mixed-composite type equations to a second-order equation with an unknown function on the right side, and this method is now widely used.

Research on the spectral theory of composite and mixed-composite type operators began under the leadership and direct participation of T.J. Juraev and continues to be carried out by his students.

T.J. Juraev made a worthy contribution to the development of the mathematical theory of the boundary layer, which is considered the most important part of modern hydrodynamics. The scientist proved that the main problems of the boundary layer for the Prandtl system of equations expressing stationary and non-stationary flows of compressible and incompressible fluids have unique solutions, and analyzed plane and three-dimensional axisymmetric flows of fluids.

T.J. Juraev is the author of 3 monographs, 4 textbooks and teaching aids, and more than 300 scientific articles published in republican and international scientific journals.

T.J. Juraev is widely known as an outstanding organizer of science and education in Uzbekistan. He headed the M.T. Urazbaev Institute of Mechanics and Seismic Resistance of Structures of the Academy of Sciences of Uzbekistan from 1974 to 1985, and the Institute of Mathematics of the Academy of Sciences of Uzbekistan from 1985 to 1992 and from 1997 to 2003. He served as Rector of Tashkent State University from 1992 to 1995, Deputy of the Oliy Majlis (Parliament) of the Republic of Uzbekistan from 1994 to 1999, and President of the Academy of Sciences of Uzbekistan from 1995 to 2000.

T.J. Juraev always combined his productive scientific work with pedagogical and public activities. He was Chairman of the "Mathematics" Council under the Academy of Sciences of Uzbekistan, Editor-in-Chief of the "Uzbekistan Mathematical Journal," President of the Uzbekistan Mathematical Society, Chairman of Scientific Councils awarding doctoral and candidate degrees at the Institute of Mechanics and Seismic Resistance of Structures, Tashkent State University, and the Institute of Mathematics of the Academy of Sciences of Uzbekistan, one of the leaders of the republican seminar on partial differential equations, and made great contributions to the development of these directions and to raising the level of mathematical research and mathematical education in Uzbekistan.

He was awarded the "Friendship" Order in 1996 and the "Glory of Labor" Order in 1999.

T.J. Juraev made a great contribution to the formation of highly qualified specialists in our republic and Central Asia; under his supervision, 8 doctors of science and more than 40 candidates of science were trained. He presented his scientific achievements in many foreign countries and at international scientific conferences. He was also chairman and member of the organizing committees of several international conferences on differential equations and mathematical physics.

T.J. Juraev visited the USA, France, Turkey, Germany, Russia, England, Austria, Hungary, Italy, Poland, Bulgaria, China, and India as part of state and scientific delegations.

A person of high human qualities, spiritually rich, faithful to his just principles, the entire multifaceted life of this outstanding scientist is a brilliant example of service to science and the people. Today, the students and followers of Tokhtamurod Juraevich are successfully working in various branches and fields of our country, as well as in foreign countries, continuing his work.

The major scientist who made a great contribution to training qualified personnel in our country, the caring mentor, the wonderful person, Academician Tokhtamurod Juraevich Juraev will always live in the memory of his friends, colleagues, students, and children.