Volume 28, Issue 2
Stability of Global Solution to Boltzmann-Enskog Equation with External Force

Commun. Math. Res., 28 (2012), pp. 108-120.

Published online: 2021-05

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• Abstract

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 stability 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 $L^1$ 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 verification of the $L^1$ stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.

• Keywords

Boltzmann-Enskog equation, global solution, stability, Lyapunov functional.

• AMS Subject Headings

76P05, 35Q75

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COPYRIGHT: © Global Science Press

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@Article{CMR-28-108, author = {Zhenglu and Jiang and and 18454 and and Zhenglu Jiang and Lijun and Ma and and 18456 and and Lijun Ma and Zheng-An and Yao and and 18457 and and Zheng-An Yao}, title = {Stability of Global Solution to Boltzmann-Enskog Equation with External Force}, journal = {Communications in Mathematical Research }, year = {2021}, volume = {28}, number = {2}, pages = {108--120}, abstract = {

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 stability 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 $L^1$ 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 verification of the $L^1$ stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.

}, issn = {2707-8523}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/cmr/19054.html} }
TY - JOUR T1 - Stability of Global Solution to Boltzmann-Enskog Equation with External Force AU - Jiang , Zhenglu AU - Ma , Lijun AU - Yao , Zheng-An JO - Communications in Mathematical Research VL - 2 SP - 108 EP - 120 PY - 2021 DA - 2021/05 SN - 28 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/cmr/19054.html KW - Boltzmann-Enskog equation, global solution, stability, Lyapunov functional. AB -

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 stability 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 $L^1$ 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 verification of the $L^1$ stability of global mild solutions to the Boltzmann-Enskog equation for a moderately or highly dense gas in the influence of external forces.

Zhenglu Jiang, Lijun Ma & Zheng-An Yao. (2021). Stability of Global Solution to Boltzmann-Enskog Equation with External Force. Communications in Mathematical Research . 28 (2). 108-120. doi:
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