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Stationary solutions of the non‐linear Boltzmann equation in a bounded spatial domain
Author(s) -
van der Mee C. V. M.,
Neunzert H.
Publication year - 1989
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670110405
Subject(s) - mathematics , bounded function , domain (mathematical analysis) , mathematical analysis , fredholm theory , boltzmann equation , contraction mapping , norm (philosophy) , boundary (topology) , contraction (grammar) , piecewise linear function , fredholm integral equation , integral equation , law , fixed point , medicine , physics , quantum mechanics , political science
A contraction mapping (or, alternatively, an implicit function theory) argument is applied in combination with the Fredholm alternative to prove the existence of a unique stationary solution of the non‐linear Boltzmann equation on a bounded spatial domain under a rather general reflection law at the piecewise C 1 boundary. The boundary data are to be small in a weighted L ∞ ‐norm.