## Abstract

We devise Lyapunov functionals and prove uniform L^{1} 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 language | English (US) |
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Pages (from-to) | 65-92 |

Number of pages | 28 |

Journal | Communications in Mathematical Physics |

Volume | 239 |

Issue number | 1-2 |

DOIs | |

State | Published - Aug 1 2003 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics

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