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Jacques-Louis Lions

Jacques-Louis Lions 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 Jacques-Louis Lions rather than just read about it. In short: Jacques-Louis Lions (French: [ʒak lwi ljɔ̃ːs]; 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 prize in 1986 and numerous other distinctions.

Jacques-Louis Lions — main illustration
Jacques-Louis Lions — illustration

Key takeaways

  • Jacques-Louis Lions belongs to mathematics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Jacques-Louis Lions to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Jacques-Louis Lions from memory before moving on to harder problems.

Reference excerpt

Jacques-Louis Lions (French: [ʒak lwi ljɔ̃ːs]; 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 prize in 1986 and numerous other distinctions. Lions is listed as an ISI highly cited researcher. He has successively taught at several universities, including the prestigious École Polytechnique and Collège de France. He is also the father of mathematician Pierre-Louis Lions, a professor at the Collège de France and recipient of the Fields Medal in 1994.

Biography Lions was born in Grasse in southern France. He attended École normale supérieure in Paris in 1947 after being part of the French Résistance in 1943 and 1944. Lions received his PhD under Laurent Schwartz. He became a professor of mathematics at the University of Nancy, the Faculty of Sciences of Paris, and the École Polytechnique. In 1966 he sent an invitation to Gury Marchuk, the soviet mathematician to visit Paris. This was hand delivered by Général De Gaulle during his visit to Akademgorodok in June of that year. He joined the prestigious Collège de France as well as the French Academy of Sciences in 1973. In 1979, he was appointed director of the Institut National de la Recherche en Informatique et Automatique (INRIA), where he taught and promoted the use of numerical simulations using finite elements integration. Throughout his career, Lions insisted on the use of mathematics in industry, with a particular involvement in the French space program, as well as in domains such as energy and the environment. This eventually led him to be appointed director of the Centre National d'Etudes Spatiales (CNES) from 1984 to 1992. Lions was elected President of the International Mathematical Union in 1991 and also received the Japan Prize and the Harvey Prize that same year. In 1992, the University of Houston awarded him an honorary doctoral degree. He was elected president of the French Academy of Sciences in 1996 and was also a Foreign Member of the Royal Society (ForMemRS) and numerous other foreign academies. He has left a considerable body of work, among this more than 400 scientific articles, 20 volumes of mathematics that were translated into English and Russian, and major contributions to several collective works, including the 4000 pages of the monumental Mathematical analysis and numerical methods for science and technology (in collaboration with Robert Dautray), as well as the Handbook of numerical analysis in 7 volumes (with Philippe G. Ciarlet). His son Pierre-Louis Lions is also a well-known mathematician who was awarded a Fields Medal in 1994. Both father and son have received honorary doctorates from Heriot-Watt University in 1986 and 1995 respectively.

Books with Enrico Magenes: Problèmes aux limites non homogènes et applications. 3 vols., 1968, 1970 Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. 1968 with L. Cesari: Quelques méthodes de résolution des problèmes aux limites non linéaires. 1969 with Robert Dautray: Mathematical analysis and numerical methods for science and technology. 9 vols., 1984/5; translated from Analyse mathématique et calcul numérique pour le sciences et le techniques by Ian Sneddon as editor with Philippe Ciarlet: Handbook of numerical analysis. 7 vols. with Alain Bensoussan, Papanicolaou: Asymptotic analysis of periodic structures. North Holland 1978 with Roland Glowinski and Raymond Trémolières: Numerical analysis of variational inequalities, North Holland 1981 2011 pbk edition Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués: Contrôlabilité exacte. Vol. tome 1. Masson. 1988. ISBN 9782225814778. Contrôlabilité exacte, perturbations et stabilisation de systèmes distribués: Perturbations. Vol. tome 2. Masson. 1988. ISBN 9782225814747. with John E. Lagnese: Modelling Analysis and Control of Thin Plates.

See also Ehrling's lemma Inverse problem Titchmarsh convolution theorem Variational inequality List of second-generation Mathematicians

References

External links Obituary on SIAM Obituary in Automatica Archived 19 March 2016 at the Wayback Machine O'Connor, John J.; Robertson, Edmund F., "Jacques-Louis Lions", MacTutor History of Mathematics Archive, University of St Andrews Jacques-Louis Lions at the Mathematics Genealogy Project

Illustrations

Jacques-Louis Lions illustration

Worked examples

Example 1 — a first encounter with Jacques-Louis Lions

Start with the simplest possible case. Write down what Jacques-Louis Lions 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 Jacques-Louis Lions 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 Jacques-Louis Lions 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 Jacques-Louis Lions

In research
Jacques-Louis Lions 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 Jacques-Louis Lions 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
Jacques-Louis Lions is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1928 births, 2001 deaths, 20th-century French mathematicians, so understanding it makes those chapters shorter.
In everyday life
Look for Jacques-Louis Lions 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 Jacques-Louis Lions in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Jacques-Louis Lions means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Jacques-Louis Lions out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Jacques-Louis Lions in simple terms?

Jacques-Louis Lions (French: [ʒak lwi ljɔ̃ːs]; 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 prize in 1986 and numerous other d…

Why does Jacques-Louis Lions 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 Jacques-Louis Lions?

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 Jacques-Louis Lions.

Tags

  • 1928 births
  • 2001 deaths
  • 20th-century French mathematicians
  • 21st-century French mathematicians
  • CNES presidents
  • Foreign members of the Chinese Academy of Sciences
  • Foreign members of the Royal Society
  • Foreign members of the Russian Academy of Sciences
  • Foreign members of the USSR Academy of Sciences
  • French fellows of the Royal Society
  • French mathematical analysts
  • International members of the National Academy of Sciences

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