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Stability of Global Solution to Boltzmann-Enskog Equation with External Force 被引量:1

Stability of Global Solution to Boltzmann-Enskog Equation with External Force
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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. 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.
出处 《Communications in Mathematical Research》 CSCD 2012年第2期108-120,共13页 数学研究通讯(英文版)
基金 The NSF (11171356) of China the Grant (09LGTY45) of Sun Yat-Sen University
关键词 Boltzmann-Enskog equation global solution STABILITY Lyapunov func-tional Boltzmann-Enskog equation, global solution, stability, Lyapunov func-tional
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