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Global existence for two‐velocity models of the Boltzmann equation
Author(s) -
Illner R.,
Neunzert H.
Publication year - 1979
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.1670010205
Subject(s) - mathematics , boltzmann equation , infinity , initial value problem , mathematical analysis , matrix (chemical analysis) , existence theorem , physics , materials science , composite material , quantum mechanics
If A is a symmetric 2 × 2‐matrix,then the initial value problemdescribes the evolution in time of a fictive gas whose particles can move only with the velocities u 1 and v 2 . It is proved that, for continuous initial values vanishing at infinity, (1) has a global solution if an H ‐Theorem holds for the gas described by (1). The validity of an H ‐Theorem is expressed by the properties of A .