Zur Seitennavigation oder mit Tastenkombination für den accesskey-Taste und Taste 1 
Zum Seiteninhalt oder mit Tastenkombination für den accesskey und Taste 2 
  1. SoSe 2023
  2. Hilfe
  3. Sitemap
Switch to english language
Startseite    Anmelden     
Logout in [min] [minutetext]

Die Veranstaltung wurde 2 mal im Vorlesungsverzeichnis SoSe 2023 gefunden:
Mastervorlesung: Kinetic Transport Theory for dilute gases    Sprache: englisch    Belegpflicht
Nr.:  102571     Vorlesung     SoSe 2023     4 SWS     jedes 2. Semester    
   Fachbereich: Fachbereich 10 Mathematik und Informatik    
   Studiengang   Master/Mathematics, PO 20 (88F23)
   Zugeordnete Lehrperson:   Pirner verantwort
   Termin: Montag   12:00  -  14:00    woch
Beginn : 03.04.2023    Ende : 03.07.2023
      Raum :   SRZ 205   Orléans-Ring 12  
  Mittwoch   14:00  -  16:00    woch
Beginn : 05.04.2023    Ende : 05.07.2023
      Raum :   SRZ 205   Orléans-Ring 12  

Content: In physics, if we want to describe the time evolution of a gas, there are different possibilities to do so. One is to imagine that the gas consists of a lot of particles and describe the time evolution of the position and the velocity of each particle by Newton's law (microscopic description). This ansatz has the advantage that it is very exact. But it has the disadvantage that in a gas we have of the order of 10^13 particles. These are too much equations to solve with a computer. But in many cases, it is even not necessary to know all the positions and velocities of every single particle. Therefore another ansatz is to describe the time evolution of macroscopic quantities as density, mean velocity and temperature (macroscopic description). This ansatz has the advantage that now we have less equations, only equations for the density, the mean velocity and the temperature. But it is only an averaged description. So it does not take into account the individual effect of the interactions of the particles. So if something happens on the level of particles which influences the macroscopic behavior, this is not a good description anymore. Therefore, there is a third possibility introduced by Boltzmann. Here, one still uses an averaged description, so it is not necessary to follow each single particle, but it is still possible to take into account the effect of interactions (kinetic description), for example the Boltzmann equation. Such a description, for example is used in a plasma. In this lecture, we will consider

  • connection of the microscopic, the kinetic and the macroscopic description and basic mathematical concepts how to get from one to another
  • Examples of models for different applications (hard-spheres, plasma, aerosols)
  • notions of solutions in the kinetic description and basic concepts to study existence of solutions in the kinetic description 
  • basic concepts to study the qualitative behavior of solutions and the convergence to equilibrium in the kinetic description

This lecture is intended for Master students who want to specialize in the field of analysis and partial differential equations. A background on partial differential equations is useful, but not mandatory.