On the well-posedness of the Boltzmann's moment system of equations in fourth approximation
Loading...
Date
2016-05
Authors
Issagali, Aizhan
Journal Title
Journal ISSN
Volume Title
Publisher
Nazarbayev University School of Science and Technology
Abstract
We study the one-dimensional non-linear non-stationary Boltzmann's moment system of equations in fourth approxi-
mation with the tools developed by Sakabekov in [4],[5] and [6]. For the third approximation system Sakabekov proves the
mass conservation law (cf. Theorem 2.1 in [4]) and discusses the existence and uniqueness of the solution (cf. Theorem
in [6]). We extend the analysis of the existence and uniqueness of the solution to the fourth approximation system. In
particular, for the fourth approximation system we discuss the well-posed initial and boundary value problem and obtain
the a-priori estimate of the solution belonging to the space of functions, continuous in time and square summable by spatial
variable.
Description
Keywords
Boltzmann equation, moment system, initial and boundary value problem, hyperbolic partial differential equations, a-priori estimate
Citation
Aizhan Issagali. 2016. On the well-posedness of the Boltzmann's moment system of equations in fourth approximation. Nazarbayev University. Capstone Project. Report. http://nur.nu.edu.kz/handle/123456789/1558