Luc Tartar

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Luc Charles Tartar (* 1946 ) is a French mathematician who studies partial differential equations.

Tartar prepared in the Lycée Charlemagne in Paris for the entrance exams of the Grand Ecoles and studied physics and mathematics at the École polytechnique from 1965 with the original goal of becoming an engineer, where he heard from Laurent Schwartz and Jacques-Louis Lions . He received his PhD in 1971 from Lions at the University of Paris (interpolation non linear et applications). He conducted research at the University of Paris IX (Dauphiné) and the University of Paris-South in Orsay . From 1975 to 1982 he conducted research in Limeil for the CEA . He later became a professor at Carnegie-Mellon University .

He has been developing mathematical methods since the 1970s to see how partial differential equations, used on the microscopic level in atomic physics and continuum mechanics, transform on higher scales into new effective theories (homogenization). This expresses his view that the dynamic laws usually used in theoretical physics, based on simple principles such as symmetries, deviate considerably from the actual laws on different scales. From a mathematical point of view, he views both stochastic models and non-relativistic quantum mechanics with skepticism (the latter because the relativity theory favors hyperbolic PDE). For example, he summarized his philosophy in his lecture at the ICM in Kyoto in 1990 and presented it in several textbooks that he wrote after his retirement. For immediate applications it is based on questions of continuum mechanics, for example in the case of mixtures and composite materials, their effective constitutive equations and the behavior of non-linear vibrations.

To study the homogenization of partial differential equations, he introduced H-measures , where H stands for homogenization, initially to describe the effects of concentration in the propagation of singularities and small oscillations of some partial differential equations in continuum mechanics. They were introduced independently by Patrick Gérard as microlocal defect measures .

In 1990 he was invited speaker at the International Congress of Mathematicians in Kyoto ( H-measures and applications ). He is a member of the Académie des sciences .

Fonts

  • General theory of homogenization - a personal introduction, Springer Verlag 2009
  • From hyperbolic systems to kinetic theory: a personalized quest, Springer Verlag 2008
  • An introduction to Sobolev spaces and interpolation spaces, Springer Verlag 2007
  • An introduction to Navier-Stokes equation and oceanography, Springer Verlag 2006
  • An introduction to the homogenization method in optimal design, in Kawohl, Tartar u. a. Optimal Shape Design , Lecture Notes in Mathematics 1740 (CIME Summer School, Portugal 1998), Springer Verlag 2000
  • On Mathematical Tools for Studying Partial Differential Equations of Continuum Physics: H-measures and Young Measures, in: G. Buttazzo, GP Galdi, L. Zanghirati (Eds.): Developments in Partial Differential Equations and Applications to Mathematical Physics, Plenum Press, New York, 1992., 201-217
  • H-measures, a New Approach for Studying Homogenization, Oscillations and Concentration Effects in Partial Differential Equations, Proc. Roy. Soc. Edinburgh, 115A, 1990, 193-230.

Web links

Individual evidence

  1. ↑ Date of birth according to Tartar From hyperbolic systems to kinetic theory , Springer 2008, p. 43, biographical footnote
  2. ^ Mathematics Genealogy Project
  3. ↑ see below
  4. ↑ Online, pdf ( Memento of the original dated February 2, 2014 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. @1@ 2Template: Webachiv / IABot / www.mathunion.org
personal data
SURNAME Tartar, Luc
ALTERNATIVE NAMES Tartar, Luc Charles (full name)
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH 1946