Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

Yanchao Li; Mingying Zhong

doi:10.3934/krm.2023004

Article Contents

2023, Volume 16, Issue 5: 676-716. Doi: 10.3934/krm.2023004

This issue Previous Article The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials Next Article Analysis of kinetic models for label switching and stochastic gradient descent

Green's function and pointwise behaviors of the one-dimensional modified Vlasov-Poisson-Boltzmann system

Yanchao Li^1, and
Mingying Zhong^2, ,

1.
School of Physical Science and Technology, Guangxi University, China
2.
School of Mathematics and Information Sciences, Guangxi University, China

^*Corresponding author: Mingying Zhong
^*Corresponding author: Mingying Zhong

Received: December 2022

Early access: February 2023

Published: October 2023

The authors are supported by the National Science Fund for Excellent Young Scholars No. 11922107, the National Natural Science Foundation of China grants No. 12171104, and Guangxi Natural Science Foundation No. 2019JJG110010

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Abstract

The pointwise space-time behaviors of the Green's function and the global solution to the modified Vlasov-Poisson-Boltzmann (mVPB) system in one-dimensional space are studied in this paper. It is shown that, the Green's function admits the diffusion wave, the Huygens's type sound wave, the singular kinetic wave and the remainder term decaying exponentially in space-time. These behaviors are similar to the Boltzmann equation (Liu and Yu in Comm. Pure Appl. Math. 57: 1543-1608, 2004). Furthermore, we establish the pointwise space-time nonlinear diffusive behaviors of the global solution to the nonlinear mVPB system in terms of the Green's function.

Keywords:

modified Vlasov-Poisson-Boltzmann system,
Green's function,
pointwise behavior,
spectrum analysis.

Mathematics Subject Classification: Primary: 76P05, 82C40; Secondary: 82D05.

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