Uniform $L^1$ stability of the inelastic Boltzmann equation with large external force for hard potentials

Shaofei Wu; Mingqing Wang; Maozhu Jin; Yuntao Zou; Lijun Song

doi:10.3934/dcdss.2019068

Article Contents

2019, Volume 12, Issue 4&5: 1005-1013. Doi: 10.3934/dcdss.2019068 open access

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Uniform $L^1$ stability of the inelastic Boltzmann equation with large external force for hard potentials

1.
Hubei Province Key Laboratory of Intelligent Robots, School of Computer Science and Engineering, Wuhan Institute of Technology, Wuhan, China
2.
Wuhan inCarCloud Technologies Pte.Ltd. China
3.
Business School, Sichuan University, Chengdu, China
4.
Wuhan Winphone Technology Co., Ltd, China
5.
Chengdu University of Information Technology, Chengdu 610225, China

* Corresponding author: Shaofei Wu
* Corresponding author: Shaofei Wu

Received: June 2017

Revised: November 2017

Published: March 2019

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Abstract

In this paper, we will study the uniform $L^1$ stability of the inelastic Boltzmann equation. More precisely, according to the existence result on the inelastic Boltzmann equation with external force near vacuum, we obtain the uniform $L^1$ stability estimates of mild solution for the hard potentials under the assumptions on the characteristic generated by force term which can be arbitrarily large. The proof is based on the exponentially decay estimate and Lu's trick in [10].

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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