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Archive for Rational Mechanics and Analysis

, Volume 194, Issue 1, pp 253–282 | Cite as

Upper Maxwellian Bounds for the Spatially Homogeneous Boltzmann Equation

  • I. M. GambaEmail author
  • V. Panferov
  • C. Villani
Article

Abstract

For the spatially homogeneous Boltzmann equation with cutoff hard potentials, it is shown that solutions remain bounded from above uniformly in time by a Maxwellian distribution, provided the initial data have a Maxwellian upper bound. The main technique is based on a comparison principle that uses a certain dissipative property of the linear Boltzmann equation. Implications of the technique to propagation of upper Maxwellian bounds in the spatially-inhomogeneous case are discussed.

Keywords

Boltzmann Equation Comparison Principle Linear Boltzmann Equation Moment Inequality Collision Kernel 

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Copyright information

© Springer-Verlag 2009

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of Texas at AustinAustinUSA
  2. 2.Department of Mathematics and StatisticsMcMaster UniversityHamiltonCanada
  3. 3.UMPA, ENS LyonLyon Cedex 07France

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