### Abstract

Large-time behavior of solutions of the one-dimensional discrete Boltzmann equation is studied. Under suitable assumptions it is proved that as time tends to infinity, the solution approaches a function which is constructed explicitly in terms of the self-similar solutions of the Burgers equation and the linear heat equation.

Original language | English |
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Pages (from-to) | 563-589 |

Number of pages | 27 |

Journal | Communications in Mathematical Physics |

Volume | 109 |

Issue number | 4 |

DOIs | |

Publication status | Published - Dec 1 1987 |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics

### Cite this

*Communications in Mathematical Physics*,

*109*(4), 563-589. https://doi.org/10.1007/BF01208958

**Large-time behavior of solutions of the discrete Boltzmann equation.** / Kawashima, Shuichi.

Research output: Contribution to journal › Article

*Communications in Mathematical Physics*, vol. 109, no. 4, pp. 563-589. https://doi.org/10.1007/BF01208958

}

TY - JOUR

T1 - Large-time behavior of solutions of the discrete Boltzmann equation

AU - Kawashima, Shuichi

PY - 1987/12/1

Y1 - 1987/12/1

N2 - Large-time behavior of solutions of the one-dimensional discrete Boltzmann equation is studied. Under suitable assumptions it is proved that as time tends to infinity, the solution approaches a function which is constructed explicitly in terms of the self-similar solutions of the Burgers equation and the linear heat equation.

AB - Large-time behavior of solutions of the one-dimensional discrete Boltzmann equation is studied. Under suitable assumptions it is proved that as time tends to infinity, the solution approaches a function which is constructed explicitly in terms of the self-similar solutions of the Burgers equation and the linear heat equation.

UR - http://www.scopus.com/inward/record.url?scp=0001482755&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001482755&partnerID=8YFLogxK

U2 - 10.1007/BF01208958

DO - 10.1007/BF01208958

M3 - Article

AN - SCOPUS:0001482755

VL - 109

SP - 563

EP - 589

JO - Communications in Mathematical Physics

JF - Communications in Mathematical Physics

SN - 0010-3616

IS - 4

ER -