Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (6): 1662-1668.

• Articles • Previous Articles     Next Articles

Regularity of the Solution to the Dissipative Linear Boltzmann Equation

 JIN Shou-Bo, CHEN Pan-Feng, SUN Shan-Hui   

  1. 1.Laboratory of Intelligent Information Processing, Suzhou University, Anhui Suzhou 234000;
    2.School of Mathematics and Statistics, Suzhou University, Anhui Suzhou 234000
  • Received:2010-11-24 Revised:2011-12-06 Online:2011-12-25 Published:2011-12-25
  • Supported by:

    宿州学院智能信息处理实验室开放课题(2011YKF12, 2011YKF14)和安徽省高校优秀青年人才基金(2011SQRL153)资助

Abstract:

This paper discusses a linear Boltzmann equation describing dissipative interactions of a gas of test particles with a fixed background. For a pseudo-Maxwellian collision kernel, it is proved that, if the initial distribution has finite  temperature and f0(v)∈H(R3),  the solution f(v, t)  of Boltzmann equation belongs to Sobolev space H(R3).

Key words: Linear Boltzmann equation, Regularity, Sobolev space, Fourier transform

CLC Number: 

  • 35Q58
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