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 language||English (US)|
|Number of pages||28|
|Journal||Communications in Mathematical Physics|
|State||Published - Aug 1 2003|
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics