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On the asymptotic behaviour and stability of the solution for the Broadwell model of the Boltzmann equation in three dimensions
Author(s) -
Toscani G.,
Neunzert H.
Publication year - 1985
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.1670070123
Subject(s) - mathematics , boltzmann equation , a priori and a posteriori , initial value problem , stability (learning theory) , mathematical analysis , fixed point theorem , function (biology) , exponential stability , thermodynamics , physics , philosophy , epistemology , machine learning , evolutionary biology , biology , computer science , nonlinear system , quantum mechanics
The initial value problem for the full Broadwell model, in gas kinetic theory, is investigated. By means of a fixed point theorem an upper estimate for the solution is derived, provided that the initial values satisfy suitable a priori conditions. Since this estimate is function of the time, the asymptotic behaviour of the global solution is determined.