Aleksei Fedorovich Filippov ( September 29, 1923 , Moscow - October 10, 2006 , Moscow ) - Russian and Soviet mathematician , author of the well-known collection of problems on ordinary differential equations (first edition - 1961).
| Alexey Fedorovich Filippov | |||||||||
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| Scientific field | Mathematics , differential equations | ||||||||
| Place of work | Moscow State University | ||||||||
| Alma mater | MSU (mehmat) | ||||||||
| Academic degree | Doctor of Physical and Mathematical Sciences | ||||||||
| Academic rank | Professor | ||||||||
| supervisor | I. G. Petrovsky | ||||||||
| Known as | mathematician , author of a collection of problems on differential equations | ||||||||
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Content
Biography
Born September 29, 1923 in Moscow, in a family of teachers of deaf-mute children. In 1941 he graduated from high school. From June 1942 to September 1946 he served in the Red Army at a research and testing ground. In 1946, he was demobilized as a junior lieutenant and entered the Faculty of Mechanics and Mathematics of Moscow State University , which he graduated in 1950, having passed exams for the first two courses in the first year [1] .
In 1953 he graduated from the graduate school of the Faculty of Mechanics and Mathematics, defended his thesis “The Flat Problem of Elastic Wave Diffraction” (supervisor - I. G. Petrovsky , with the participation of S. L. Sobolev ) [1] and was left at the department of differential equations of this faculty . In 1976 he defended his doctoral dissertation “Wave diffraction on polyhedra” [1] .
From 1953 until the end of his life he worked at the Department of Differential Equations of the Mechanics and Mathematics Faculty of Moscow State University, from 1955 - as an assistant professor, from 1978 - as a professor. He has published over 70 scientific papers and several monographs, and has read a number of compulsory and special courses on differential equations [1] .
Recognition and memory
- He was awarded the MV Lomonosov Prize (1993) for his brilliant lecture skills and the creation of the textbook “A Collection of Problems in Differential Equations”, which was reprinted many times.
- He was awarded the title of Honored Professor of Moscow State University (1996).
Scientific activity
Research Interests:
- differential equations
- diffraction theory
- differential equations with discontinuous right-hand side,
- differential inclusions
- optimal control
- finite difference equations , numerical methods for solving differential equations.
The main scientific achievements of A.F. Filippov include:
- the introduction of the concept of stability of a difference scheme (together with V. S. Ryaben'ky ) and the proof of the fundamental fact that approximation and stability imply convergence ( Filippov-Ryaben'ky theorem ). [2] [3] The book of V. S. Ryaben'ky and A. F. Filippov “On the stability of difference equations” (1956) is the first monograph in the world on the stability of difference schemes. [four]
- Filippov 's lemma on the existence of a measurable selector of a many-valued map and the theorem on the existence of optimal control based on it for a wide class of problems in the theory of controlled systems . [five]
- application of the apparatus of differential inclusions for the study of differential equations with discontinuous right-hand side and optimal control. [6] [7]
Books
- Ryaben'ky V. S. , Filippov A. F. On the stability of difference equations. - M .: Gostekhizdat , 1956.
- A.F. Filippov. Collection of problems on differential equations. - Ed. 1st. - M .: Fizmatgiz , 1961 .-- 100 p.
- A.F. Filippov. Collection of problems on differential equations. - Ed. 5th. - M .: Nauka, 1979.- 128 p. - 68,000 copies.
- A.F. Filippov. Collection of problems on differential equations . - Ed. 8th. - M .: Integral-Press, 1998 .-- 208 p. - ISBN 5896020104 .
- A.F. Filippov. Collection of problems on differential equations. - Izhevsk: Regular and chaotic dynamics, 2000. - 176 p. - ISBN 5939720080 .
- A.F. Filippov. Collection of problems on differential equations . - LCI, 2008 .-- 240 p. - ISBN 9785382004556 .
- A.F. Filippov. Differential equations with discontinuous right-hand side. - M .: Science, 1985.
- A.F. Filippov. Introduction to the theory of differential equations. - Ed. 1st. - Editorial URSS, 2004 .-- 240 p. - ISBN 5354004160 .
- A.F. Filippov. Introduction to the theory of differential equations . - Ed. 2nd. - Editorial URSS, 2007 .-- 240 p.
Rewards
Medals:
- For the victory over Germany in the Great Patriotic War of 1941-1945.
- veteran of labour
- For valiant work. In commemoration of the centenary of the birth of V.I. Lenin
- Anniversary medal "Twenty Years of Victory in the Great Patriotic War of 1941-1945."
- Anniversary medal "Thirty Years of Victory in the Great Patriotic War of 1941-1945."
- Anniversary medal “Forty years of Victory in the Great Patriotic War of 1941-1945.”
- Anniversary medal "50 years of Victory in the Great Patriotic War of 1941-1945."
- Anniversary medal "60 years of Victory in the Great Patriotic War of 1941-1945."
- Prize winner M.V. Lomonosova (1993)
- Honorary title " Honored Professor of Moscow State University " (1996).
Interesting Facts
One of the first published works of A. F. Filippov was an elementary proof of Jordan's theorem [8] .
Links
- Filippov, Alexey Fedorovich
- A. F. Filippov on the site "Biography.ru"
- All-Russian Mathematical Portal
- Aleksei Fedorovich Filippov (On the occasion of the 75th birthday). Differential Equations, vol. 34, No. 10 (1998), p. 1299-1303
- All-Russian Scientific Conference “A. F. Filippov - man, scientist, teacher . ”
- Memories of A.F. Filippov . The Seven Arts Journal, N 2 (83), February 2017
Notes
- ↑ 1 2 3 4 Memoirs of A.F. Filippov . The Seven Arts Journal, N 2 (83), February 2017
- ↑ V.S. Ryaben'ky, A.F. Filippov. On the stability of difference equations. M., Gostekhizdat, 1956.
- ↑ K.I. Babenko. Fundamentals of numerical analysis. M .: Science. 1986.
- ↑ V.S. Ryaben'ky. Personal page
- ↑ A.F. Filippov. On some questions of the theory of optimal regulation. Bulletin of Moscow State University, Mat. and fur., N2 (1959), pp. 25-32.
- ↑ A.F. Filippov. Differential equations with discontinuous right-hand side. M., Science, 1985.
- ↑ V.I. Blagodatskikh, A.F. Filippov. Differential inclusions and optimal control. Tr. Steklov., T. 169 (1985) .
- ↑ A.F. Filippov. An elementary proof of Jordan's theorem , UMN, 5: 5 (39) (1950), 173–176