Lyapunov Functionals and L1-Stability for Discrete Velocity Boltzmann Equations

被引:0
作者
Seung-Yeal Ha
Athanasios E. Tzavaras
机构
[1] University of Wisconsin-Madison,Department of Mathematics
[2] Institute for Applied and Computational Mathematics,undefined
[3] FORTH,undefined
来源
Communications in Mathematical Physics | 2003年 / 239卷
关键词
Phase Space; Weak Solution; Source Term; Boltzmann Equation; Velocity Model;
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学科分类号
摘要
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 L1 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.
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页码:65 / 92
页数:27
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