BOUNDEDNESS OF THE STATIONARY SOLUTION TO THE BOLTZMANN EQUATION WITH SPATIAL SMEARING, DIFFUSIVE BOUNDARY CONDITIONS, AND LIONS' COLLISION KERNEL

被引：1

作者：

Loebus, Joerg-Uwe ^{[1
,2
]}

机构：

[1] Linkopings Univ, Matemat Inst, SE-58183 Linkoping, Sweden

[2] Martin Luther Univ Halle Wittenberg, Inst Math, D-06099 Halle, Germany

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2018年 / 50卷 / 06期

关键词：

Boltzmann equation; stationarity; spatial smearing; diffusive boundary conditions; Lions' collision kernel; UPPER MAXWELLIAN BOUNDS; REGULARITY;

D O I：

10.1137/17M1160446

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We investigate the Boltzmann equation with spatial smearing, diffusive boundary conditions, and Lions' collision kernel. Both the physical as well as the velocity space, are assumed to be bounded. Existence and uniqueness of a stationary solution, which is a probability density, has been demonstrated in [S. Caprino, M. Pulvirenti, and W. Wagner, SIAM T. Math. Anal., 29 (1998), pp. 913-934] under a certain smallness assumption on the collision term. We prove that whenever there is a stationary solution then it is a.e. positively bounded from below and above.

引用

页码：5761 / 5782

页数：22

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