Jean Jacques Moreau (31 July 1923 – 9 January 2014) was a French mathematician and mechanician. He normally published under the name J. J. Moreau. Moreau was born in

Blaye Blaye (; ) is a commune and subprefecture in the Gironde department in Nouvelle-Aquitaine in southwestern France. For centuries, Blaye was a particularly convenient crossing point for those who came from the north and went to Bordeaux or fur ...

. He received his doctorate in mathematics from the

University of Paris The University of Paris (), known Metonymy, metonymically as the Sorbonne (), was the leading university in Paris, France, from 1150 to 1970, except for 1793–1806 during the French Revolution. Emerging around 1150 as a corporation associated wit ...

, then became a researcher at the

Centre National de la Recherche Scientifique The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

. He was appointed Professor of Mathematical Models in Physics at

Poitiers University The University of Poitiers (UP; , ) is a public university located in Poitiers, France. It is a member of the Coimbra Group. It is multidisciplinary and contributes to making Poitiers the city with the highest student/inhabitant ratio in France ...

and later Professor of General Mechanics at

University of Montpellier II Montpellier 2 University (Université Montpellier 2) was a French university in the '' académie'' of Montpellier. It was one of the three universities formed in 1970 from the original University of Montpellier. In January 2015, Montpellier 1 Un ...

. He was emeritus professor in the Laboratoire de Mécanique et Génie Civil, a joint research unit of the university and the CNRS. Moreau's principal works have been in non-smooth mechanics and

convex analysis Convex analysis is the branch of mathematics devoted to the study of properties of convex functions and convex sets, often with applications in convex optimization, convex minimization, a subdomain of optimization (mathematics), optimization theor ...

. He is considered one of the founders of convex analysis, where several fundamental and now classical results have his name (Moreau's lemma of the two cones, Moreau's envelopes, Moreau-Yosida's approximations, Fenchel-Moreau's theorem, etc.). He founded the Convex Analysis Group in the 1970s at Montpellier University (France). He may also be considered as the father of non-smooth mechanics, a field of

Solid Mechanics Solid mechanics (also known as mechanics of solids) is the branch of continuum mechanics that studies the behavior of solid materials, especially their motion and deformation (mechanics), deformation under the action of forces, temperature chang ...

dealing with mechanical systems subjected to unilateral and bilateral constraints, impacts and set-valued friction laws (like Coulomb's friction law and its variations). He was the first to introduce complementarity conditions in Lagrangian systems, and to prove that the Gauss' principle of mechanics extends to the case of non-smooth mechanics (one C.R.A.S. Paris paper in 1963 and a SIAM Control J. article in 1966). He invented in 1971/1972 the so-called sweeping process, which is a specific

differential inclusion In mathematics, differential inclusions are a generalization of the concept of ordinary differential equation of the form :\frac(t)\in F(t,x(t)), where ''F'' is a multivalued map, i.e. ''F''(''t'', ''x'') is a ''set'' rather than a single point ...

whose right-hand side is the normal cone to a time or state-dependent set (that may be convex or not). Sweeping processes represent a nice and powerful mathematical framework for many non-smooth mechanical systems, including Lagrangian systems, with applications in plasticity, fluid mechanics, electrical circuits with non-smooth components, etc. The mathematical literature on various kinds of sweeping processes has become abundant, with extensions towards non-convex sets (especially prox-regular sets), state-dependent sets, higher-order processes with distributional solutions, relationships with complementarity dynamical systems, etc. After retiring in the 1980s, he started an intense research activity in Granular Matter, and contributed to settle the so-called Moreau-Jean event-capturing (or time-stepping) numerical scheme. The Moreau-Jean scheme may be seen as an extension of the implicit Euler method, originating from the (second order) sweeping process formalism of the Lagrange dynamics with unilateral constraints and impacts, which is a specific Measure Differential Inclusion (i.e., a differential inclusion whose solutions are measures). The Moreau-Jean scheme has inspired several groups of researchers in Europe and the USA for the simulation of non-smooth mechanical systems, and is available in open-source software packages like the INRIA SICONOS platform or the LMGC90 platform. He discovered the helicity invariant in the

fluid dynamics In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion ...

ideal fluid In physics, a perfect fluid or ideal fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure . Real fluids are viscous ("sticky") and contain (and conduct) heat. Perfect fluids are id ...

s in 1962. Moreau received many prizes, including the Grand Prix Joannidès of the

Académie des Sciences The French Academy of Sciences (, ) is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French Scientific method, scientific research. It was at the forefron ...

References

Sources

* "A short biography of Jean Jacques Moreau", in P. Alart, O. Maisonneuve, R.T. Rockafellar, ''Nonsmooth mechanics and analysis: theoretical and numerical advances'' (proceedings of a symposium in J.J. Moreau's honor), 2005,
p. 11''ff''
* M. Kunze and M.D.P. Monteiro Marques, "An introduction to Moreau's sweeping process", in B. Brogliato (Ed.) "Impacts in Mechanical Systems. Analysis and Modeling", Springer Verlag, Lecture Notes in Physics 551, 2000, pp. 1–60. * M.D.P. Monteiro Marques, "Differential Inclusions in Nonsmooth Mechanical Problems. Shocks and Dry Friction", Progress in Nonlinear Differential Equations and their Applications, Birkhauser, vol.9, 1993. * V. Acary and B. Brogliato, "Numerical Methods for Nonsmooth Dynamical Systems. Applications in Mechanics and Electronics", Springer Verlag, Lecture Notes in Applied and Computational Mechanics, vol.35, 2008. * SICONOS: http://siconos.gforge.inria.fr/ * LMGC90: https://git-xen.lmgc.univ-montp2.fr/lmgc90/lmgc90_user

Links

Some of J.J. Moreau'
publications
{{DEFAULTSORT:Moreau, Jean Jacques 1923 births 2014 deaths 20th-century French mathematicians University of Paris alumni