Communications in Mathematical Sciences

Volume 15 (2017)

Number 3

Stability analysis of a class of globally hyperbolic moment system

Pages: 609 – 633

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n3.a3

Authors

Weifeng Zhao (Beijing Computational Science Research Center, Beijing, China)

Wen-An Yong (Zhou Pei-Yuan Center for Applied Mathematics, Tsinghua University, Beijing, China; and Beijing Computational Science Research Center, Beijing, China)

Li-Shi Luo (Department of Mathematics and Statistics, Old Dominion University, Norfolk, Virginia, U.S.A.; and Beijing Computational Science Research Center, Beijing, China)

Abstract

This work studies the stability of a class of the globally hyperbolic moment system (GHMS) with the single relaxation-time collision model in the sense of hyperbolic relaxation systems. We prove the equilibrium stability of the GHMS in both one- and multi-dimensional space. For a five-moment system in one dimension, we prove its linear instability for some quiescent nonequilibrium states and demonstrate numerically the nonlinear instability of the nonequilibrium states.

Keywords

globally hyperbolic moment system, hyperbolic relaxation systems, stability criteria

2010 Mathematics Subject Classification

35B35, 35L60, 82C40

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Published 24 February 2017