DEPARTMENT OF EQUATIONS OF MATHEMATICAL PHYSICS SUSU

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The Department of Equations of Mathematical Physics was established by A. L. Shestakov`s Order  90, 10.05.2006, the South-Urals State University Rector. Professor G. A. Sviridyuk was appointed the head of the Mathematical Physics Equations Department. Professor V. E. Fedorov, S. A. Zagrebina, A. A. Zamyshlyaeva, N. A. Manakova, O. A. Ruzakova, V. I. Ushakov, the Chief Lecturer D. E. Shafranov have become the first employees of the department. A. F. Gilmutdinova has become the first post-graduate student as well as A. A. Bayazitova has become the first graduate.


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Right now you can make a small digression into the history of basic subjects which are traditionally taught at the Mathematical Physics Equations Department in Classical universities.

Mathematical Physics is a pure mathematical science indeed, it differs from Geometry as it is based on the knowledge of nature not axioms. Archimedes, an ancient scientist and warrior (282-212 B.C.) is truly considered to be the founder of the Mathematical Physics Equations. It was he who discovered a number of physical laws such as the law of a lever, the law of floating of bodies and others and Archimedes used them successfully not only in practice but also in mathematical constructions.

Mathematical Physics got a mighty impulse in the XVIII century after I. Newton (1643-1727) and G. Leibniz (1646-1716) had invented the methods of Mathematical analyses. The works of the Pleiades of outstanding scientists J. Bernoulli (1700-1782), L. Euler (1707-1783), G. dAlembert (1717-1783), G. Lagrange (1736-1813), P. Laplace, G. Fourier (1768-1830), S. Poisson (1781-1840) put basis for the theory of classical mathematical physics equation typical representatives of which are the equations of heat-conducting, wave equations and the equations of Laplace and Poisson.

In the XIX century the equations of mathematical physics got a solid basis due to the development of methods of analyses and grounding mathematical analysis. In theories apart from the formulas giving the solutions of the equations in important but particular cases the results of the analytical character appear such as the theorem about the existence of solutions, the principle of maximum and others. Thanks to the brilliant works of mathematicians of that time A. Cauchy (1789-1857), L. Dirichlet (1805-1859), K. Weierstrass (1815-1897), S. V. Kovalevskaya (1850-1891) the new theory of the equations with particular derivatives singled out from mathematical physics.

In the XXth century the equations with particular derivatives having experienced beneficial influence of the arising mathematical theories (harmonical and functional analyses, the theory of Lie groups and others) change into a very strong and branching science, which is in the appendices of different branches of natural science. This particular science made it possible the flight of a man into space (Yu. A. Gagarin, 1961) and landing people on the Moon (N. Armstrong, A. Oldrin, 1969). Nowadays the theory of equations with particular derivatives is an inalienable part of classical university education in the field of mathematics, information science and physics.

Lets call the names of the outstanding Russian mathematicians whose fundamental works of the world level made up the basis of modern subjects of the profile of the department. They are I. G. Petrovsky (1901-1973) and O. A. Oleinik (1925-2001), V. I. Smirnov (1887-1974) and O. A. Ladyzchenskaya (1922-2004), A. N. Tikhonov (1906-1993) and A. A. Samarsky (1919-2008).

In the late XIX early XX century in the writings of H. Poincare (1854-1912), C. G. Rossby (1898-1957), and many others began to appear non-classical equations of mathematical physics. Their systematic study began in the fundamental work of Sobolev (1908-1989) in the mid 50's of the last century. Currently, especially the rapidly developing one of the domains of non-classical equations of mathematical physics the Sobolev type equations. In Russia, this direction is represented by G. V. Demidenko, N. A. Sidorov, M. V. Falaleev, M. V. Fokin and many others. And abroad by R. E. Showalter, A. Favini, A. Yagi and many others. At the department under the leadership of Sviridyuk the Scientific School was formed. Its main purpose is to study in different aspects Sobolev type equations and the development of their applications. One of the latest achievements of the school is the creation (in cooperation with A. L. Shestakov) theory of optimal measuring, in which model-based Shestakov Sviridyuk restored dynamically distorted signals.

 


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