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Existence and Uniqueness of the Solution of the Non‐stationary Boltzmann‐Equation for the Electrons in a Collision Dominated Plasma by Means of Operator Semigroups
Author(s) -
Bartolomäus G.,
Wilhelm J.
Publication year - 1981
Publication title -
annalen der physik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.009
H-Index - 68
eISSN - 1521-3889
pISSN - 0003-3804
DOI - 10.1002/andp.19814930306
Subject(s) - boltzmann equation , uniqueness , bounded function , semigroup , physics , operator (biology) , collision , mathematical analysis , boltzmann constant , boundary (topology) , mathematics , quantum mechanics , computer science , biochemistry , chemistry , computer security , repressor , transcription factor , gene
Based on the semigroup approach a new proof is presented of the existence of a unique solution of the non‐stationary Boltzmann‐equation for the electron component of a collision dominated plasma. All interactions can be included which yield bounded collision operators. The electric and magnetic fields were permitted to be inhomogeneous in space, and the investigations were performed for a bounded plasma. It has been shown that the Boltzmann‐operator is the infinitesimal generator of a strongly continuous operator‐semigroup which uniquely determines the nonnegative solution from a given initial function taking into account the given boundary conditions.