摘要:

We study the stationary half-space linearized Boltzmann equation with a force term decaying to zero at infinity. We extend to this case the results of Bardos, Cafiisch and Nicolaenko for a gas of hard spheres without external force, namely we prove existence, uniqueness and asymptotic properties of the solution. Our analysis includes the case of hard potentials.

ISSN:0041-1450    

DOI:10.1080/00411459808205139

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

The existence of weak shock wave solutions for discrete velocity models of the Boltzmann equation is proved. Specifically, consider triples (M−M+,c) of two Maxwellians M−M+and shock speeds c ∈ ℛ satisfying the Rankine-Hugoniot conditions. The triple (M−, M−, c) satisfies these conditions trivially for anyc. Ifc0is chosen to be such that the manifold defined by the Rankine-Hugoniot conditions exhibits a transcritical bifurcation at C0, then we prove that there is a one-sided, one-parameter family of triplesM−, M+()andc(), with M+(0) =M−and c(0) = c0, such that there is a rarefied shock wave solution for the discrete velocity model connectingM−with M+(), moving with shock speed c(), and satisfying the entropy condition.

ISSN:0041-1450    

DOI:10.1080/00411459808205140

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor

摘要:

Variational principles for ratios of linear neutron flux functionals are extended to treat boundary condition and boundary perturbations in nuclear systems which are described by the steady-state inhomogeneous and homogeneous Boltzmann equations. The relationship of these principles with first-order perturbation theory is established. Their applicability to perturbations of the external boundary of the system is investigated through numerical examples.

ISSN:0041-1450    

DOI:10.1080/00411459808205141

出版商:Taylor & Francis Group    

年代:1998

数据来源: Taylor