Some problems on conservation laws and VlasovPoissonBoltzmann equation
關於守恆律和 VlasovPoissonBoltzmann 方程的一些問題
Student thesis: Doctoral Thesis
Author(s)
Related Research Unit(s)
Detail(s)
Awarding Institution  

Supervisors/Advisors 

Award date  2 Oct 2009 
Link(s)
Permanent Link  https://scholars.cityu.edu.hk/en/theses/theses(e23c362cb3c24ace8db480e2310bfef0).html 

Other link(s)  Links 
Abstract
In this thesis, we studied a mathematical study of conservation laws and gas motion
under the influence of selfinduced forcing. The models considered are the 2 × 2 system
of hyperbolic conservation laws with artificial viscosity and the VlasovPoisson
Boltzmann system in kinetic theory.
First, the existence of strong travelling wave profiles for a class of 2 × 2 viscous
conservation laws is considered when the corresponding inviscid systems are hyperbolic.
Apart from some technical assumptions, the only main assumption is hyperbolicity
in accordance with which existence theory can be applied to systems which
are not strictly hyperbolic. Characteristic fields can be neither genuinely nonlinear nor
linearly degenerate.
The VlasovPoissonBoltzmann system, meanwhile, is a classical physical model
for the time evolution of charged particles. Second, the twospecies VlasovPoisson
Boltzmann system with a nonconstant background density in the whole space is investigated.
There is a stationary solution when the background density goes to zero.
The globalintime classical solutions and the nonlinear stability of solutions to the
Cauchy problem near the stationary state in some Sobolev space without any time
derivatives are constructed. The convergence rate in time to the global Maxwellian and
the uniformintime stability of solutions are also obtained using the energy method.
The macroscopic conservation laws are essentially used to deal with the a priori estimates
on both the microscopic and macroscopic parts of the solution in the proof.
Additionally, some interactive energy functionals are introduced to overcome the difficulty
that stems from notime derivatives in the energy functional.
 Conservation laws (Mathematics), Kinetic theory of gases