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

Russel Caflisch

Research output: Contribution to journalArticle

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 languageEnglish (US)
Pages (from-to)529-547
Number of pages19
JournalCommunications on Pure and Applied Mathematics
Volume38
Issue number5
DOIs
StatePublished - 1985

Fingerprint

Delta functions
Boltzmann equation
Delta Function
Boltzmann Equation
Half-space
Comparison Method
Nonlinear Boundary Value Problems
Zero
Mach number
Boundary value problems
Mathematical operators
Shock
Collision
Temperature
Operator
Profile
Form

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

Cite this

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

In: Communications on Pure and Applied Mathematics, Vol. 38, No. 5, 1985, p. 529-547.

Research output: Contribution to journalArticle

@article{a64f5f0e31be42f18b0aab8d6da1956f,
title = "The half‐space problem for the boltzmann equation at zero temperature",
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.",
author = "Russel Caflisch",
year = "1985",
doi = "10.1002/cpa.3160380506",
language = "English (US)",
volume = "38",
pages = "529--547",
journal = "Communications on Pure and Applied Mathematics",
issn = "0010-3640",
publisher = "Wiley-Liss Inc.",
number = "5",

}

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 -