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The half‐space problem for the boltzmann equation at zero temperature
Author(s) -
Caflisch Russel E.
Publication year - 1985
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160380506
Subject(s) - mathematics , boltzmann equation , zero (linguistics) , mathematical analysis , mach number , nonlinear system , function (biology) , boltzmann constant , space (punctuation) , boundary value problem , operator (biology) , distribution function , dirac delta function , shock (circulatory) , mathematical physics , physics , mechanics , quantum mechanics , philosophy , linguistics , chemistry , repressor , evolutionary biology , gene , medicine , biochemistry , transcription factor , biology
Abstract At zero temperature the Maxwellian distribution is a delta function of velocity. In this paper the Boltzmann equation is linearized around a delta function and then analyzed by a comparison method. Using these results and similar bounds for the nonlinear collision operator, a nonlinear boundary value problem at zero temperature is solved. The results are applied to the asymptotic description at the cold end of the shock profile at infinite Mach number. All solutions F are assumed to have the form F ( x , ξ) = (1 ‐ a ( x ))δ(ξ) + f ( x , ξ) in which a and f are regular functions.