一维修正Vlasov-Poisson-Boltzmann系统的Green函数和点态行为

IF 1 4区数学 Q1 MATHEMATICS

Kinetic and Related Models Pub Date : 2023-03-23 DOI:10.3934/krm.2023004

Yanchao Li, Mingying Zhong

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引用次数: 0

摘要

本文研究了一维空间中格林函数的点向时空行为和改进Vlasov- Poisson-Boltzmann (mVPB)系统的全局解。结果表明，格林函数允许扩散波、惠更斯型声波、奇异动能波和剩余项在时空中呈指数衰减。这些行为类似于玻尔兹曼方程(Liu and Yu in Comm. Pure apple)。数学。57:1543-1608,2004)。在此基础上，利用格林函数建立了非线性mVPB系统全局解的点向时空非线性扩散行为。

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

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.

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来源期刊

Kinetic and Related Models 数学-数学

CiteScore

2.10

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： KRM publishes high quality papers of original research in the areas of kinetic equations spanning from mathematical theory to numerical analysis, simulations and modelling. It includes studies on models arising from physics, engineering, finance, biology, human and social sciences, together with their related fields such as fluid models, interacting particle systems and quantum systems. A more detailed indication of its scope is given by the subject interests of the members of the Board of Editors. Invited expository articles are also published from time to time.