### 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.

Original language | English (US) |
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Pages (from-to) | 529-547 |

Number of pages | 19 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 38 |

Issue number | 5 |

DOIs | |

State | Published - Sep 1985 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Caflisch, R. E. (1985). The half‐space problem for the boltzmann equation at zero temperature.

*Communications on Pure and Applied Mathematics*,*38*(5), 529-547. https://doi.org/10.1002/cpa.3160380506