Boltzmann equation on a lattice: Existence and uniqueness of solutions

Herbert Spohn

doi:10.1007/BF01011782

Boltzmann equation on a lattice: Existence and uniqueness of solutions

Herbert Spohn

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Cercignani, Greenberg, and Zweifel proved the existence and uniqueness of solutions of the Boltzmann equation on a toroidal lattice under the assumption that the collision kernel is bounded. We give an alternative, considerably simpler, proof which is based on a fixed point argument.

Original language	English
Pages (from-to)	463-470
Number of pages	8
Journal	Journal of Statistical Physics
Volume	20
Issue number	4
DOIs	https://doi.org/10.1007/BF01011782
State	Published - Apr 1979
Externally published	Yes

Keywords

Nonlinear Boltzmann equation
lattice approximation

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10.1007/BF01011782

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title = "Boltzmann equation on a lattice: Existence and uniqueness of solutions",

abstract = "Cercignani, Greenberg, and Zweifel proved the existence and uniqueness of solutions of the Boltzmann equation on a toroidal lattice under the assumption that the collision kernel is bounded. We give an alternative, considerably simpler, proof which is based on a fixed point argument.",

keywords = "Nonlinear Boltzmann equation, lattice approximation",

author = "Herbert Spohn",

year = "1979",

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journal = "Journal of Statistical Physics",

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AB - Cercignani, Greenberg, and Zweifel proved the existence and uniqueness of solutions of the Boltzmann equation on a toroidal lattice under the assumption that the collision kernel is bounded. We give an alternative, considerably simpler, proof which is based on a fixed point argument.

KW - Nonlinear Boltzmann equation

KW - lattice approximation

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DO - 10.1007/BF01011782

M3 - Article

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SP - 463

EP - 470

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 4

ER -

Boltzmann equation on a lattice: Existence and uniqueness of solutions

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Keywords

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