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Generalized Boundary Conditions in an Existence and Uniqueness Proof for the Solution of the Non‐Stationary Electron Boltzmann Equation by Means of Operator‐Semigroups
Author(s) -
Bartolomäus G.,
Wilhelm J.
Publication year - 1983
Publication title -
beiträge aus der plasmaphysik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0005-8025
DOI - 10.1002/ctpp.19830230606
Subject(s) - semigroup , mathematics , uniqueness , boundary (topology) , boundary value problem , mathematical analysis , operator (biology) , range (aeronautics) , boltzmann equation , generator (circuit theory) , poincaré–steklov operator , function (biology) , free boundary problem , robin boundary condition , physics , biochemistry , chemistry , materials science , repressor , quantum mechanics , evolutionary biology , biology , transcription factor , composite material , gene , power (physics)
Recently, based on the semigroup approach a new proof was presented of the existence of a unique solution of the non‐stationary Boltzmann equation for the electron component of a collision dominated plasma. The proof underlies some restrictions which should be overcome to extend the validity range to other problems of physical interest. One of the restrictions is the boundary condition applied. The choice of the boundary condition is essential for the proof because it determines the range of definition of the infinitesimal generator and thus the operator semigroup itself. The paper proves the existence of a unique solution for generalized boundary conditions, this solution takes non‐negative values, which is necessary for a distribution function from the physical point of view.