The half‐space problem for the boltzmann equation at zero temperature

Russel E. Caflisch

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)529-547
Number of pages19
JournalCommunications on Pure and Applied Mathematics
Issue number5
StatePublished - Sep 1985

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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