### 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) |
---|---|

Pages (from-to) | 529-547 |

Number of pages | 19 |

Journal | Communications on Pure and Applied Mathematics |

Volume | 38 |

Issue number | 5 |

DOIs | |

State | Published - 1985 |

### Fingerprint

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

*Communications on Pure and Applied Mathematics*,

*38*(5), 529-547. https://doi.org/10.1002/cpa.3160380506

**The half‐space problem for the boltzmann equation at zero temperature.** / Caflisch, Russel.

Research output: Contribution to journal › Article

*Communications on Pure and Applied Mathematics*, vol. 38, no. 5, pp. 529-547. https://doi.org/10.1002/cpa.3160380506

}

TY - JOUR

T1 - The half‐space problem for the boltzmann equation at zero temperature

AU - Caflisch, Russel

PY - 1985

Y1 - 1985

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84990574717&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84990574717&partnerID=8YFLogxK

U2 - 10.1002/cpa.3160380506

DO - 10.1002/cpa.3160380506

M3 - Article

VL - 38

SP - 529

EP - 547

JO - Communications on Pure and Applied Mathematics

JF - Communications on Pure and Applied Mathematics

SN - 0010-3640

IS - 5

ER -