Spatially homogeneous solutions of the Vlasov-Nordstrom-Fokker-Planck system

JOURNAL OF DIFFERENTIAL EQUATIONS

卷:257

Article

Alcantara Felix, Jose Antonio¹  Calogero, Simone²  Pankavich, Stephen³ 

[1] Univ Granada, Dept Appl Math, Granada, Spain

[2] Univ Gothenburg, Chalmers Inst Technol, Dept Math, Gothenburg, Sweden

[3] Colorado Sch Mines, Dept Appl Math & Stat, Golden, CO 80401 USA

关键词: Vlasov-Nordstrom;    Fokker-Planck equation;    Spatially homogeneous;    Global existence;    Ultra-relativistic;    Long time behavior;   

DOI  :  10.1016/j.jde.2014.07.006

来源: Elsevier

【 摘 要 】

The Vlasov-Nordstrom-Fokker-Planck system describes the evolution of self-gravitating matter experiencing collisions with a fixed background of particles in the framework of a relativistic scalar theory of gravitation. We study the spatially-homogeneous system and prove global existence and uniqueness of solutions for the corresponding initial value problem in three momentum dimensions. Additionally, we study the long time asymptotic behavior of the system and prove that even in the absence of friction, solutions possess a non-trivial asymptotic profile. An exact formula for the long time limit of the particle density is derived in the ultra-relativistic case. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free