全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
Mathematics  2013 

Instantaneous filling of the vacuum for the full Boltzmann equation in convex domains

DOI: 10.1007/s00205-015-0874-x

Full-Text   Cite this paper   Add to My Lib

Abstract:

We prove the immediate appearance of a lower bound for mild solutions to the full Boltzmann equation in the torus or a $C^2$ convex domain with specular boundary conditions, under the sole assumption of continuity away from the grazing set of the solution. These results are entirely constructive if the domain is $C^3$ and strictly convex. We investigate a wide range of collision kernels, some satisfying Grad's cutoff assumption and others not. We show that this lower bound is exponential, independent of time and space with explicit constants depending only on the \textit{a priori} bounds on the solution. In particular, this lower bound is Maxwellian in the case of cutoff collision kernels. A thorough study of characteristic trajectories, as well as a geometric approach of grazing collisions against the boundary are derived.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133