Stability of Global Solution to Boltzmann-Enskog Equation with External Force
Stability of Global Solution to Boltzmann-Enskog Equation with External Force作者机构:Department of Mathematics Sun Yat-Sen University Guangzhou 510275 School of Mathematics Hebei University of Technology Tianjin 300501
出 版 物:《Communications in Mathematical Research》 (数学研究通讯(英文版))
年 卷 期:2012年第28卷第2期
页 面:108-120页
核心收录:
学科分类:12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 081104[工学-模式识别与智能系统] 08[工学] 070104[理学-应用数学] 0835[工学-软件工程] 0701[理学-数学] 0811[工学-控制科学与工程] 0812[工学-计算机科学与技术(可授工学、理学学位)]
基 金:The NSF (11171356) of China the Grant (09LGTY45) of Sun Yat-Sen University
主 题:Boltzmann-Enskog equation global solution stability Lyapunov func-tional
摘 要:In the presence of external forces depending only on the time and space variables, the Boltzmann-Enskog equation formally conserves only the mass of the . system, and its entropy functional is also nonincreasing. Corresponding to this type of equation, we first give some hypotheses of its bicharacteristic equations and then get some results about the stablity of its global solution with the help of two new Lyapunov functionals: one is to describe interactions between particles with different velocities and the other is to measure the L1 distance between two mild solutions. The former Lyapunov functional yields the time-asymptotic convergence of global classical solutions to the collision free motion while the latter is applied into the veri-fication of the L1 stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.