Mark Vishik (mathematician)

Mark Vishik (also Marko Vishik, Russian: Марк(o) Иосифович Вишик, * October 19, 1921 in Lviv) is a mathematician from Lwów / Lemberg / Lvov / Lviv, who works in the field of Partial Differential Equations.

Life and work

Lwów

In Lwów, Mark Vishik visited the fifth gymnasium (high school), which specialized in physics and mathematics. His mathematical talent was encouraged by a method of teaching, which left it up to the students to find mathematical proofs. He began studying mathematics at the University of Lvov in December 1939, at the time when the Lwów school mathematics was still active. Among his teachers were Juliusz Schauder, Stanisław Mazur, Bronislaw Knaster, and Edward Szpilrajn, who organized a student conference in 1940 in Lwów, also attended by Stefan Banach.^[1]

From Lwów to Tbilisi

In June 1941, during the occupation of Lwów the Germans, Vishik left the city with a Komsomol group. Vishik then joined the retreating army and on foot reached Ternopil and then Zhmerynka (in Vinnytsia) and in two more weeks got by means of a freight train to Kiev. After fleeing further to Krasnodar, Vishik passed Dniprodzerzhynsk and for two months helped with the harvest in Timashevsk. He was a student at the pedagogical university in Krasnodar, but because of advancing German troops he then fled further to Makhachkala, where he studied for a year. He fell ill with malaria, but managed to hide on a military train in the fall of 1942 and reached Tbilisi. Vishik was already acquainted with Nikoloz Muskhelishvili, mathematician and president in 1941, founded the Georgian Academy of Sciences, whom he met during Muskhelishvili's visit to Lwów (probably in 1940) and was therefore ready to start studying in Tbilisi. The Mathematical Institute was run by Ilia Vekua there were lectures by V. Kupradze. Vishik became friend with the number theorist Arnold Walfisz. After graduating in 1943, Vishik was advised by Walfisz, Gantmacher, and Muskhelishvili to go to Moscow to continue his studies.

Moscow

Since the spring of 1945, he studied in Moscow under supervision by Lazar Lyusternik. On May 8, 1945 (V-E-Day), he met his future wife Asya Guterman. He received his doctorate in 1947 at the Steklov Institute and defended his thesis under I.G. Petrovsky and S.L. Sobolev. His dissertation is a generalization of the work The method of orthogonal projection in potential theory by Hermann Weyl (Duke Math J. 7, 1940), which he read with no knowledge of English. From 1947 to 1965 he was assistant, and then, after his habilitation in 1951, a Professor at the Moscow Power Engineering Institute.

Since 1965, Vishik has been a professor at the Faculty of Mechanics and Mathematics, Lomonosov University in Moscow. Since 1993 he conducts research at the Institute for Information Transmission Problems of the Russian Academy of Sciences. Mark Vishik has 48 students and is the author of several books and more than 250 articles. His two sons, Mikhail and Simeon, are also mathematicians. Since 1961, he organized his seminar at the Moscow State University on Partial Differential Equations.

His work was exceptionally fruitful. For example, Jacques-Louis Lions and w:it:Enrico Magenes wrote a three-volume work on non-homogeneous boundary value problems, developing the work by Mark Vishik and Sergey Sobolev from 1956.

Awards

Mark Vishik is a member of the Russian Academy of Sciences (since 1990) and the Italian Academy of Sciences (since 1994). In 2001 he received an Honorary Doctorate from the Free University of Berlin.^[2]

Monographs

• Dissertation: On the method of orthogonal projections for linear self-adjoint equations, 1947
• Habilitation: On systems of elliptic differential equations and on general boundary-value problems, 1951
• (With AV Fursikov): Mathematical Problems of Statistical Hydromechanics, Kluwer, 1988.
• (With AV Babin): Attractors of Evolution Equations, North-Holland, 1992 (Russisches Original 1989)
• Asymptotic Behaviour of Solutions of Evolutionary Equations, Cambridge University Press, 1993
• (Author and editor with AV Babin): Properties of Global Attractors of Partial Differential Equations, Advances in Soviet Mathematics (AMS), Volume 10, 1992 (anthology of four articles, two of Mark Vishik (with Skvortsov VY))
• (With VV Chepyzhov): Attractors for Equations of Mathematical Physics (Colloquium Publications 49 (AMS)), 2002

See also

• Short biography in Russian
• Publications of Mark Vishik
• The Mathematics Genealogy Project - Mark Vishik
• Mark Iosifovich Vishik (on his sixtieth birthday), MS Agranovich et al., Russian Mathematical Surveys 37 (4), 1982 al., Russian Mathematical Surveys 37 (4), 1982
• MS Agranovich et al., Mathematical Life. Mark Iosifovich Vishik (on his seventy-fifth birthday). Russian Mathematical Surveys 52, 1997, online
• Mathematical Symposium in Honor of Professor Mark Vishik's 80th birthday
• Roger Temam, Mark Vishik and his work
• Partial differential equations, M.S. Agranovich and M.A. Shubin (editors), American Mathematical Society Translations, Series 2, vol. 206. Mark Vishik's Seminar, Papers dedicated to Vishik on the occasion of his 80th birthday, Advances in the Mathematical Sciences, 51, American Mathematical Society, Providence, RI, 2002.
• M.S. Agranovich, Mark Vishik's Seminar at Moscow State University. Amer. Math. Soc. Transl. (2) vol. 206 (2002), 239—253
• Discrete and Continuous Dynamical Systems 10, Volume 1 / 2, 2004 (Partial Differential Equations and Applications, A special volume in honor of Mark Vishik's 80th birthday).
• WB Demidovich: interview in June 2007, p. 68-93 online

References

1. ^ M.S. Agranovich et al. (1997). "Mathematical Life. Mark Iosifovich Vishik (on his seventy-fifth birthday)". Russian Mathematical Surveys 52. http://www.mathnet.ru/php/getFT.phtml?jrnid=rm&paperid=1594&what=fullt. 
2. ^ Mathematical Symposium in Honor of Professor Mark Vishik http://dynamics.mi.fu-berlin.de/vishik-symposium/