Titelaufnahme

Titel
Diffusive approximation of the Liouville equation / von Gottfried Hastermann
VerfasserHastermann, Gottfried
Begutachter / BegutachterinArnold, Anton
Erschienen2014
Umfang54 Bl. : graph. Darst.
HochschulschriftWien, Techn. Univ., Dipl.-Arb., 2014
SpracheEnglisch
DokumenttypDiplomarbeit
Schlagwörter (EN)vanishing viscosity / diffusive Liouville equation / eixstence of solution
URNurn:nbn:at:at-ubtuw:1-63606 Persistent Identifier (URN)
Zugriffsbeschränkung
 Das Werk ist frei verfügbar
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Diffusive approximation of the Liouville equation [0.92 mb]
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Zusammenfassung (Englisch)

In statistical physics phase space behavior of an ensemble of non interacting particles can be described by the Liouville equation. In the stationary case with inflow boundary conditions on a (finite) slab the method of characteristics provides solutions with jump type discontinuities. The goal of this work was to overcome the uniqueness issues using a vanishing viscosity method. Since existing results cannot handle problems with non symmetric, parameter dependent collision operators, these approaches are extended. In particular existence of an unique solution to the parabolic-elliptic degenerated diffusive version of the stationary Liouville equation is proven. Furthermore some basic properties such as smoothness and a bound by the posed boundary conditions were established. Hereby the intrinsic Krein space structure of this problem was pointed out.