Stability of Maxwellian states for the Broadwell model of the extended Boltzmann equation

  • M. Miklavčič
  • G. Spiga


The extended Boltzmann equation for test particles in an absorbing and generating background plane medium with generalized boundary conditions is discretized according to the classical Broadwell scheme, which allows three dimensions to the molecular velocity vector. Stability of Maxwellian states to small space dependent perturbations is studied analytically and numerically, both on the whole real line and on a finite interval. Results prove, among other things, existence, for the boundary value problem, of regions of positive measure in the parameter space which yield instability, due to the presence of a positive eigenvalue.

Key words. Kinetic theory, Boltzmann equation, discrete velocity methods, stability of equilibria. 


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Copyright information

© Birkhäuser Verlag, Basel, 1998

Authors and Affiliations

  • M. Miklavčič
    • 1
  • G. Spiga
    • 2
  1. 1.Department of Mathematics, Michigan State University, East Lansing, Michigan 48824, USA. e-mail: milan@math.msu.eduUS
  2. 2.Department of Mathematics, University of Parma, Via M. D'Azeglio 85, 43100 Parma, Italy. e-mail: spiga@prmat.math.unipr.itIT

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