Mark Vishik
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Mark Vishik (also Marko Vishik, ; 19 October 1921,
Lwów Lviv ( or ; ; ; see #Names and symbols, below for other names) is the largest city in western Ukraine, as well as the List of cities in Ukraine, fifth-largest city in Ukraine, with a population of It serves as the administrative centre of ...
, II Rzeczpospolita – 23 June 2012) was a
Soviet The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...
mathematician who worked in the field of
partial differential equations In mathematics, a partial differential equation (PDE) is an equation which involves a multivariable function and one or more of its partial derivatives. The function is often thought of as an "unknown" that solves the equation, similar to how ...
.


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 Lviv The Ivan Franko National University of Lviv (named after Ivan Franko, ) is a state-sponsored university in Lviv, Ukraine. Since 1940 the university is named after Ukrainian poet Ivan Franko. The university is the oldest institution of highe ...
in December 1939, at the time when the Lwów school mathematics was still active. Among his teachers were
Juliusz Schauder Juliusz Paweł Schauder (; 21 September 1899 – September 1943) was a Polish mathematician known for his work in functional analysis, partial differential equations and mathematical physics. Life and career Born on 21 September 1899 in Lwów ...
,
Stanisław Mazur Stanisław Mieczysław Mazur (; 1 January 1905 – 5 November 1981) was a Polish mathematician and a member of the Polish Academy of Sciences. Mazur made important contributions to geometrical methods in linear and nonlinear functional analysis ...
, Bronislaw Knaster, and Edward Szpilrajn, who organized a student conference in 1940 in Lviv, also attended by
Stefan Banach Stefan Banach ( ; 30 March 1892 – 31 August 1945) was a Polish mathematician who is generally considered one of the 20th century's most important and influential mathematicians. He was the founder of modern functional analysis, and an original ...
.


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 Ternopil, known until 1944 mostly as Tarnopol, is a city in western Ukraine, located on the banks of the Seret River. Ternopil is one of the major cities of Western Ukraine and the historical regions of Galicia and Podolia. The populatio ...
and then
Zhmerynka Zhmerynka (, ) is a city in Vinnytsia Oblast, central Ukraine. It serves as the administrative center of Zhmerynka Raion within the oblast. Population: It is located in the historic region of Podolia. Name There are many propositions as far as ...
(in
Vinnytsia Vinnytsia ( ; , ) is a city in west-central Ukraine, located on the banks of the Southern Bug. It serves as the administrative centre, administrative center of Vinnytsia Oblast. It is the largest city in the historic region of Podillia. It also s ...
) and in two more weeks got by means of a freight train to
Kiev Kyiv, also Kiev, is the capital and most populous List of cities in Ukraine, city of Ukraine. Located in the north-central part of the country, it straddles both sides of the Dnieper, Dnieper River. As of 1 January 2022, its population was 2, ...
. After fleeing further to
Krasnodar Krasnodar, formerly Yekaterinodar (until 1920), is the largest city and the administrative centre of Krasnodar Krai, Russia. The city stands on the Kuban River in southern Russia, with a population of 1,154,885 residents, and up to 1.263 millio ...
, Vishik passed
Dniprodzerzhynsk Kamianske (, ; ), previously known as Dniprodzerzhynsk from 1936 to 2016, is an industrial city in Dnipropetrovsk Oblast, Ukraine, and a port on the Dnieper River. It serves as the administrative center of Kamianske Raion and Kamianske urban ...
and for two months helped with the harvest in
Timashevsk Timashevsk (), sometimes romanized Timashyovsk, is a town and the administrative center of Timashevsky District of Krasnodar Krai, Russia, located on the Kirpili River north of Krasnodar, the administrative center of the krai. As of 2020, t ...
. He was a student at the pedagogical university in
Krasnodar Krasnodar, formerly Yekaterinodar (until 1920), is the largest city and the administrative centre of Krasnodar Krai, Russia. The city stands on the Kuban River in southern Russia, with a population of 1,154,885 residents, and up to 1.263 millio ...
, but because of advancing German troops he then fled further to
Makhachkala Makhachkala, previously known as Petrovskoye (1844–1857) and Port-Petrovsk (1857–1921), or by the local Kumyk language, Kumyk name of Anji, is the capital and List of cities and towns in Russia by population, largest city of Dagestan, Russia. ...
, where he studied for a year. He fell ill with
malaria Malaria is a Mosquito-borne disease, mosquito-borne infectious disease that affects vertebrates and ''Anopheles'' mosquitoes. Human malaria causes Signs and symptoms, symptoms that typically include fever, Fatigue (medical), fatigue, vomitin ...
, but managed to hide on a military train in the fall of 1942 and reached Tbilisi. Vishik was already acquainted with
Nikoloz Muskhelishvili Nikoloz (Niko) Muskhelishvili ( ka, ნიკოლოზ (ნიკო) მუსხელიშვილი ; – 15 July 1976) was a Soviet Georgian mathematician, physicist and engineer who was one of the founders and first President (1941– ...
, 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 Arnold Walfisz (2 July 1892 – 29 May 1962) was a Jewish-Polish mathematician working in analytic number theory. Life After the ''Abitur'' in Warsaw, Poland, Arnold Walfisz studied (1909−14 and 1918−21) in Germany at Munich, Berlin, Heidel ...
. 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 the supervision of
Lazar Lyusternik Lazar Aronovich Lyusternik (also Lusternik, Lusternick, Ljusternik; ; 31 December 1899 – 22 July 1981) was a Soviet mathematician. He is famous for his work in topology and differential geometry, to which he applied the variational principle. U ...
. On May 8, 1945 ( V-E-Day), he met his future wife Asya Guterman. He received his doctorate in 1947 at the
Steklov Institute of Mathematics Steklov Institute of Mathematics or Steklov Mathematical Institute () is a premier research institute based in Moscow, specialized in mathematics, and a part of the Russian Academy of Sciences. The institute is named after Vladimir Andreevich Stek ...
, and defended his thesis under Ivan G. Petrovsky and Sergey L. Sobolev. His dissertation was a generalization of the work ''The method of orthogonal projection in potential theory'' by
Hermann Weyl Hermann Klaus Hugo Weyl (; ; 9 November 1885 – 8 December 1955) was a German mathematician, theoretical physicist, logician and philosopher. Although much of his working life was spent in Zürich, Switzerland, and then Princeton, New Jersey, ...
, 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 National Research University "Moscow Power Engineering Institute" (MPEI; ) is a public university based in Moscow, Russia. It offers training in the fields of Power Engineering, Electric Engineering, Radio Engineering, Electronics, Information ...
. Since 1965, Vishik was a professor at the Faculty of Mechanics and Mathematics,
Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...
in Moscow. Since 1993 he conducted research at the Institute for Information Transmission Problems of the Russian Academy of Sciences. Vishik had 48 students and was 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 on Partial Differential Equations at Moscow State University. Vishik's work has been exceptionally fruitful. For example,
Jacques-Louis Lions Jacques-Louis Lions (; 2 May 1928 – 17 May 2001) was a French mathematician who made contributions to the theory of partial differential equations and to stochastic control, among other areas. He received the SIAM's John von Neumann Lecture p ...
and w:it:Enrico Magenes wrote a three-volume work on non-homogeneous boundary value problems, developing the work by Vishik and Sobolev from 1956.


Awards

Mark Vishik was a member of the
Italian Academy of Sciences The Accademia Nazionale delle Scienze (), or more formally L'Accademia Nazionale delle Scienze detta dei XL, and also called the Accademia dei XL (), is Italy's national academy of science. Its offices are located within the Villino Rosso, at the co ...
since 1994. In 2001 he received an Honorary Doctorate from the
Free University of Berlin The Free University of Berlin (, often abbreviated as FU Berlin or simply FU) is a public university, public research university in Berlin, Germany. It was founded in West Berlin in 1948 with American support during the early Cold War period a ...
.


Seminar series

Vishik started his seminar at
Moscow State University Moscow State University (MSU), officially M. V. Lomonosov Moscow State University,. is a public university, public research university in Moscow, Russia. The university includes 15 research institutes, 43 faculties, more than 300 departments, a ...
in the spring of 1961, at the suggestion of I. M. Gelfand. The seminar ran on Mondays in Room 13-06 of the main building of Moscow State University, starting at 18:00 (initially at 16:00) and lasting for several hours. It featured talks of many world class mathematicians from Russia, France, and other countries. Traditionally, the speakers of the seminars were guests at M. I. Vishik's apartment on the Sunday night, before the seminar. The seminar ran for more than 50 years, until Mark Vishik's death in June 2012. Mark Iosifovich considered this seminar one of the main achievements of his life. This seminar collected the color of the mathematical community, and speaking at its meetings was considered a great honour.


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 A.V. Fursikov): ''Mathematical Problems of Statistical Hydromechanics'', Kluwer, 1988. * (With A.V. 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 A.V. 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 V.Y. Skvortsov)) *(With V.V. Chepyzhov): ''Attractors for Equations of Mathematical Physics'' (Colloquium Publications 49 (AMS)), 2002


See also

*
Séminaire Nicolas Bourbaki The (from French: Bourbaki Seminar) is a series of seminars (in fact public lectures with printed notes distributed) that has been held in Paris since 1948. It is one of the major institutions of contemporary mathematics, and a barometer of m ...
*
French mathematical seminars French mathematical seminars have been an important type of institution combining research and exposition, active since the beginning of the twentieth century. From 1909 to 1937, the Séminaire Hadamard gathered many participants (f. i. André We ...


References


External links


Short biography in RussianPublications of Mark Vishik
*''Mark Iosifovich Vishik (on his sixtieth birthday)'', MS Agranovich ''et al.'',
Russian Mathematical Surveys ''Uspekhi Matematicheskikh Nauk'' () is a Russian mathematical journal, published by the Russian Academy of Sciences and Moscow Mathematical Society and translated into English as ''Russian Mathematical Surveys''. ''Uspekhi Matematicheskikh Nauk' ...
37 (4), 1982 al., Russian Mathematical Surveys 37 (4), 1982 * M.S. Agranovich ''et al.'', '' Mathematical Life. Mark Iosifovich Vishik (on his seventy-fifth birthday)''.
Russian Mathematical Surveys ''Uspekhi Matematicheskikh Nauk'' () is a Russian mathematical journal, published by the Russian Academy of Sciences and Moscow Mathematical Society and translated into English as ''Russian Mathematical Surveys''. ''Uspekhi Matematicheskikh Nauk' ...
52, 1997
onlineMathematical Symposium in Honor of Professor Mark Vishik's 80th birthdayInternational Conference "Partial Differential Equations and Applications" in Honour of Mark Vishik on the occasion of his 90th birthdayRoger 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). * W.B. Demidovich: interview in June 2007, p. 68-9
online


{{DEFAULTSORT:Vishik, Mark 1921 births 2012 deaths Politicians from Lviv Academic staff of Moscow State University Soviet mathematicians Partial differential equation theorists Steklov Institute of Mathematics alumni