Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory

Tadeusz Platkowski; Reinhard Illner

doi:10.1137/1030045

Discrete Velocity Models of the Boltzmann Equation: A Survey on the Mathematical ASPECTS of the Theory

SIAM Review ◽

10.1137/1030045 ◽

1988 ◽

Vol 30 (2) ◽

pp. 213-255 ◽

Cited By ~ 140

Author(s):

Tadeusz Platkowski ◽

Reinhard Illner

Keyword(s):

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

Lattice points on circles and discrete velocity models for the Boltzmann equation

SIAM Journal on Mathematical Analysis ◽

10.1137/040618916 ◽

2006 ◽

Vol 37 (6) ◽

pp. 1903-1922 ◽

Cited By ~ 18

Author(s):

Laura Fainsilber ◽

Pär Kurlberg ◽

Bernt Wennberg

Keyword(s):

Boltzmann Equation ◽

Lattice Points ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

On the sizes of discrete velocity models of the Boltzmann equation for mixtures

Computational Mathematics and Mathematical Physics ◽

10.1134/s0965542507060103 ◽

2007 ◽

Vol 47 (6) ◽

pp. 998-1006 ◽

Cited By ~ 3

Author(s):

S. Z. Adzhiev ◽

V. V. Vedenyapin

Keyword(s):

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

On the discrete velocity models of the Boltzmann equation in several dimensions

Annali di Matematica Pura ed Applicata (1923 -) ◽

10.1007/bf01762549 ◽

1984 ◽

Vol 138 (1) ◽

pp. 297-308 ◽

Cited By ~ 7

Author(s):

G. Toscani

Keyword(s):

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

Discrete velocity models and the Boltzmann equation

Trends and Applications of Pure Mathematics to Mechanics - Lecture Notes in Physics ◽

10.1007/3-540-12916-2_57 ◽

1984 ◽

pp. 188-193

Author(s):

Reinhard Illner

Keyword(s):

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

Entropy profiles in discrete velocity models of the Boltzmann equation

Transport Theory and Statistical Physics ◽

10.1080/00411458908204322 ◽

1989 ◽

Vol 18 (2) ◽

pp. 221-234 ◽

Cited By ~ 7

Author(s):

T. Platkowski

Keyword(s):

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

On shock wave solutions for discrete velocity models of the Boltzmann equation

Transport Theory and Statistical Physics ◽

10.1080/00411459808205140 ◽

1998 ◽

Vol 27 (1) ◽

pp. 35-66 ◽

Cited By ~ 6

Author(s):

C. Bose ◽

R. Illner ◽

S. Ukai

Keyword(s):

Shock Wave ◽

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

Wave Solutions ◽

The Boltzmann Equation

Download Full-text

Instability and stability of numerical approximations to discrete velocity models of the Boltzmann equation

Quarterly of Applied Mathematics ◽

10.1090/qam/1417239 ◽

1996 ◽

Vol 54 (4) ◽

pp. 777-791 ◽

Cited By ~ 1

Author(s):

Robert Peszek

Keyword(s):

Boltzmann Equation ◽

Numerical Approximations ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

Global Existence and Stability of Solutions for Discrete Velocity Models of the Boltzmann Equation

North-Holland Mathematics Studies - Recent Topics in Nonlinear PDE ◽

10.1016/s0304-0208(08)71492-0 ◽

1984 ◽

pp. 59-85 ◽

Cited By ~ 10

Author(s):

Shuichi Kawashima

Keyword(s):

Boltzmann Equation ◽

Global Existence ◽

Stability Of Solutions ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation ◽

Existence And Stability

Download Full-text

Normal, high order discrete velocity models of the Boltzmann equation

Computers & Mathematics with Applications ◽

10.1016/j.camwa.2017.09.024 ◽

2018 ◽

Vol 75 (2) ◽

pp. 503-519 ◽

Cited By ~ 2

Author(s):

Stefan Brechtken ◽

Thomas Sasse

Keyword(s):

Boltzmann Equation ◽

High Order ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text

Approximation of the Boltzmann equation by discrete velocity models

Journal of Statistical Physics ◽

10.1007/bf02180142 ◽

1995 ◽

Vol 78 (5-6) ◽

pp. 1555-1570 ◽

Cited By ~ 4

Author(s):

Wolfgang Wagner

Keyword(s):

Boltzmann Equation ◽

Discrete Velocity Models ◽

Discrete Velocity ◽

Velocity Models ◽

The Boltzmann Equation

Download Full-text