mathematics

Mark Vishik

Mark Vishik is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Mark Vishik rather than just read about it. In short: Mark Vishik (also Marko Vishik Russian: Марко Иосифович Вишик; 19 October 1921–23 June 2012) was a Poland-born Soviet and Russian mathematician who worked 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.

Key takeaways

Mark Vishik belongs to mathematics; place it in that map before memorising details.
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Reference excerpt

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 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 Lviv, also attended by Stefan Banach.

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 the supervision of 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 of Mathematics, 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, 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 was a professor at the Faculty of Mechanics and Mathematics, Moscow State University 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 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 since 1994. In 2001 he received an Honorary Doctorate from the Free University of Berlin.

Seminar series Vishik started his seminar at Moscow State University 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 French mathematical seminars

References

External links Short biography in Russian Publications of 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 M.S. 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 International Conference "Partial Differential Equations and Applications" in Honour of Mark Vishik on the occasion of his 90th 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). W.B. Demidovich: interview in June 2007, p. 68-93 online Mark Vishik's seminar

Worked examples

Example 1 — a first encounter with Mark Vishik

Start with the simplest possible case. Write down what Mark Vishik claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Mark Vishik before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Mark Vishik ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Mark Vishik

In research: Mark Vishik appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Mark Vishik in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Mark Vishik is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1921 births, 2012 deaths, Academic staff of Moscow State University, so understanding it makes those chapters shorter.
In everyday life: Look for Mark Vishik outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Mark Vishik in 20 minutes

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Frequently asked questions

What is Mark Vishik in simple terms?

Mark Vishik (also Marko Vishik Russian: Марко Иосифович Вишик; 19 October 1921–23 June 2012) was a Poland-born Soviet and Russian mathematician who worked in the field of partial differential equations. Life and work Lwów In Lwów, Mark Vishik visited the fifth gymnasium (high school), which special…

Why does Mark Vishik matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Mark Vishik?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Mark Vishik.