Moreau was born in Blaye. He received his doctorate in mathematics from the University of Paris, then became a researcher at the Centre National de la Recherche Scientifique. He was appointed Professor of Mathematical Models in Physics at Poitiers University and later Professor of General Mechanics at University of Montpellier II. 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. 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 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 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.
Moreau received many prizes, including the Grand Prix Joannidès of the Académie des Sciences.
Referencesedit
^(PDF). Archived from the original (PDF) on 21 September 2018. Retrieved 4 February 2014.
Sourcesedit
"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, ISBN0-387-29196-2 p. 11ff
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.
jean, jacques, moreau, jean, jacques, moreau, july, 1923, january, 2014, french, mathematician, mechanician, normally, published, under, name, moreau, jean, jacques, moreaujean, jacques, moreau, flèche, circa, 1954born, 1923, july, 1923blaye, francedied9, janu. Jean Jacques Moreau 31 July 1923 9 January 2014 1 was a French mathematician and mechanician He normally published under the name J J Moreau Jean Jacques MoreauJean Jacques Moreau in La Fleche circa 1954Born 1923 07 31 31 July 1923Blaye FranceDied9 January 2014 2014 01 09 aged 90 Montpellier FranceNationalityFrenchScientific careerFieldsMechanics Mathematics Moreau was born in Blaye He received his doctorate in mathematics from the University of Paris then became a researcher at the Centre National de la Recherche Scientifique He was appointed Professor of Mathematical Models in Physics at Poitiers University and later Professor of General Mechanics at University of Montpellier II He was emeritus professor in the Laboratoire de Mecanique et Genie Civil a joint research unit of the university and the CNRS Moreau s principal works have been in non smooth mechanics and convex analysis 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 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 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 of ideal fluids in 1962 Moreau received many prizes including the Grand Prix Joannides of the Academie des Sciences References edit ISIMM Newsletter No 2 of January 30 2014 PDF Archived from the original PDF on 21 September 2018 Retrieved 4 February 2014 Sources edit 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 ISBN 0 387 29196 2 p 11ff 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 userLinks editSome of J J Moreau s publications Retrieved from https en wikipedia org w index php title Jean Jacques Moreau amp oldid 1142994152, wikipedia, wiki, book, books, library,
