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SUMMARY:A.V. Borovskikh\, K.S. Platonova (MSU\, Moscow\, Russia)
DTSTART:20231019T110000Z
DTEND:20231019T120000Z
DTSTAMP:20260423T021327Z
UID:mmandim/61
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/mmandim/61/"
 >Group analysis of the one-dimentional kinetic equation and the problem of
  closing the moment system</a>\nby A.V. Borovskikh\, K.S. Platonova (MSU\,
  Moscow\, Russia) as part of Mathematical models and integration methods\n
 \n\nAbstract\nThe report is devoted to a problem that goes back to the wor
 ks of Maxwell and Clausius\, the relationship between the kinetic equation
 s of the particles of the medium and the macroscopic characteristics of th
 e medium. In the modern form\, the question is how to obtain the equations
  of a continuum media from the kinetic equations. The fundamental problem 
 is the following: integration of the kinetic equation with power-law weigh
 ts over velocities gives an infinite system of equations\, the first of wh
 ich are very similar to the equations of a continuous medium. But the syst
 em of equations of a continuous medium is finite. This means that the infi
 nite system must be truncated and closed. The problem consists of two ques
 tions: where to truncate and what ratio use to close. The report will pres
 ent an approach based on group methods. The idea is to calculate the symme
 try group of the kinetic equation\, transfer its action to macroscopic qua
 ntities\, find invariants already in terms of macroscopic quantities\, and
  use them to construct a closure. This was successfully implemented in the
  one-dimensional case\, the details will be presented in the report.\n
LOCATION:https://researchseminars.org/talk/mmandim/61/
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