摘要:

The abstract differential equation (Tf)' =−Af with “partial range” boundary conditions is solved on a Hilbert space. T and A are (possibly unbounded) self-adjoint operators, A ≥ 0 and semi-Fredholm. Examples from kinetic theory are given.

ISSN:0041-1450    

DOI:10.1080/00411458208245739

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

We study a generalized transport equation of the typewhere A is a strictly positive operator on L2(μ). Using ideas originally introduced by Beals, Larsen-Habetler, Hangelbroek and Lekkerkerker, we analyze this equation according to standard Case singular eigenfunction theory and prove existence and uniqueness of solutions for infinite and semi-infinite media.

ISSN:0041-1450    

DOI:10.1080/00411458208245740

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

We investigate the transport equationwith suitable boundary conditions through an equivalent integral equation. Assuming the incoming fluxes, the internal source term f(x,μ), the cross section c(x) and the parameter ξ to be nonnegative, we prove the existence of a unique dominant eigenvalue ξ=ξ0(τ) for which the homogeneous problem has a positive solution (critical case), the existence of a unique positive solution for ξ < ξ0(τ) (non-critical case), and the absence of positive solutions for ξ > ξ0(τ) (supercritical case). We show ξ0(τ) to decrease continuously from ∞ to some ξ0(∞)>0 whenever ξ increases from 0 to ∞ (monotonicity). The results are obtained by studying an operator that leaves invariant the cone of nonnegative functions in L∞(0,τ).

ISSN:0041-1450    

DOI:10.1080/00411458208245741

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

The solution to Kramer's equation describing Brownian motion is obtained using the multiple collision formulation. The solution is represented in terms of generalized functions; and using examples with known solutions, interpretations are given.

ISSN:0041-1450    

DOI:10.1080/00411458208245742

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

Scaling of hot electron transport in slab plasmas is proposed and discussed in the energy range 0–150 keV. Theoretical bases for slab scaling are developed and results are compared with exact Monte Carlo simulations in the Fokker-Planck representation. Simple scaling laws deduced from the analysis are useful for fast numerical application and eliminate need for repetitive computations.

ISSN:0041-1450    

DOI:10.1080/00411458208245743

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

摘要:

One simple unitary transformation is provided between the linear transport model of R. Beals and a model presented else-where. Special attention is paid to similar relationships in electron transport theory.

ISSN:0041-1450    

DOI:10.1080/00411458208245744

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor

ISSN:0041-1450    

DOI:10.1080/00411458208245745

出版商:Taylor & Francis Group    

年代:1982

数据来源: Taylor