Lyapunov functional and L1-stability for discrete velocity Boltzmann equations

Seimg Yeal Ha*, Athanasios E. Tzavaras

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

19 Scopus citations


We devise Lyapunov functionals and prove uniform L1 stability for one-dimensional semilinear hyperbolic systems with quadratic nonlinear source terms. These systems encompass a class of discrete velocity models for the Boltzmann equation. The Lyapunov functional is equivalent to the L 1 distance between two weak solutions and non-increasing in time. They result from computations of two point interactions in the phase space. For certain models with only transversal collisional terms there exist generalizations for three and multi-point interactions.

Original languageEnglish (US)
Pages (from-to)65-92
Number of pages28
JournalCommunications in Mathematical Physics
Issue number1-2
StatePublished - Aug 2003
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


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