Supports of measure solutions for spatially homogeneous boltzmann equations

Xicheng Zhang; Xianwen Zhang

doi:10.1007/s10955-006-9067-1

Supports of measure solutions for spatially homogeneous boltzmann equations

Xicheng Zhang^*, Xianwen Zhang^*

^*Corresponding author for this work

Huazhong University of Science and Technology

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

2 Citations (Scopus)

Abstract

We prove that the support of the unique measure solution for the spatially homoge-neous Boltzmann equation in R3 is the whole space, if the initial distribution is not a Dirac measure and has 4-order moment. More precisely, we obtain the lower bound of exponential type for the probability of any small ball in ³ relative to the measure solution.

Original language	English
Pages (from-to)	485-495
Number of pages	11
Journal	Journal of Statistical Physics
Volume	124
Issue number	2-4
DOIs	https://doi.org/10.1007/s10955-006-9067-1
Publication status	Published - Aug 2006
Externally published	Yes

Keywords

Boltzmann equation
Measure solution
Support

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10.1007/s10955-006-9067-1

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title = "Supports of measure solutions for spatially homogeneous boltzmann equations",

abstract = "We prove that the support of the unique measure solution for the spatially homoge-neous Boltzmann equation in R3 is the whole space, if the initial distribution is not a Dirac measure and has 4-order moment. More precisely, we obtain the lower bound of exponential type for the probability of any small ball in 3 relative to the measure solution.",

keywords = "Boltzmann equation, Measure solution, Support",

author = "Xicheng Zhang and Xianwen Zhang",

year = "2006",

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doi = "10.1007/s10955-006-9067-1",

language = "English",

volume = "124",

pages = "485--495",

journal = "Journal of Statistical Physics",

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T1 - Supports of measure solutions for spatially homogeneous boltzmann equations

AU - Zhang, Xicheng

AU - Zhang, Xianwen

PY - 2006/8

Y1 - 2006/8

N2 - We prove that the support of the unique measure solution for the spatially homoge-neous Boltzmann equation in R3 is the whole space, if the initial distribution is not a Dirac measure and has 4-order moment. More precisely, we obtain the lower bound of exponential type for the probability of any small ball in 3 relative to the measure solution.

AB - We prove that the support of the unique measure solution for the spatially homoge-neous Boltzmann equation in R3 is the whole space, if the initial distribution is not a Dirac measure and has 4-order moment. More precisely, we obtain the lower bound of exponential type for the probability of any small ball in 3 relative to the measure solution.

KW - Boltzmann equation

KW - Measure solution

KW - Support

UR - http://www.scopus.com/inward/record.url?scp=33751070516&partnerID=8YFLogxK

U2 - 10.1007/s10955-006-9067-1

DO - 10.1007/s10955-006-9067-1

M3 - Article

AN - SCOPUS:33751070516

SN - 0022-4715

VL - 124

SP - 485

EP - 495

JO - Journal of Statistical Physics

JF - Journal of Statistical Physics

IS - 2-4

ER -

Supports of measure solutions for spatially homogeneous boltzmann equations

Abstract

Keywords

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