摘要:

This is the written version of an invited presentation at the Fourteenth International Conference on Transport Theory held in Beijing, China, June 12–17, 1995.

ISSN:0041-1450    

DOI:10.1080/00411459708221782

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We present a review of the Wigner-Poisson system of equations, including its equivalence to a Schrödinger-Poisson system when such an equivalence exists, and including its relationship to the Vlasov equation in the classical limith→ 0. Existence and uniqueness for a particle cloud in all space, in a periodic setting, and with a nonlinear Poisson equation and periodic boundary conditions are all discussed. Finally, some results on asymptotic decay of solutions are mentioned for both the Wigner-Poisson system and the Vlasov-Poisson system in the repulsive case. These results are founded on an identity known in the quantum context as “pseudo-conformal conservation law”. The counterparts of this identity for the Vlasov-Poisson system and the classicalN—body problem are presented.

ISSN:0041-1450    

DOI:10.1080/00411459708221783

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

This paper presents a simple method to obtain a further result on uniqueness of mild solutions of the Cauchy problem for Boltzmann equations (without external force)

ISSN:0041-1450    

DOI:10.1080/00411459708221784

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

In this paper we generalize Kato's perturbation theory to weakly compact perturbations. As applications of this theory, we discuss the distribution of the essential spectrum of linear transport operators.

ISSN:0041-1450    

DOI:10.1080/00411459708221785

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The main aim of this paper is to investigate some aspects of the spectral properties of strongly continuous semigroups generated by linear transport operator. These properties are closely related to the large time behavior of time dependent solutions of transport equations. Our attention is focused on the transport equations with reentry boundary conditions. A class of abstract kinetic systems is studied, and, as applications, some transport equations are investigated.

ISSN:0041-1450    

DOI:10.1080/00411459708221786

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

A consistent semidiscrete model of the Boltzmann equation, constructed from the continuous scattering kernel formulation by discretizing the speed variable, is discussed in comparison with recent results on the subject.

ISSN:0041-1450    

DOI:10.1080/00411459708221787

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

The complex eigenvalue problem of a mono-energetic neutron transport operator is studied in a homogeneous sphere with spherically symmetric scattering. It is shown that the spectrum involves a countable infinity of complex eigenvalues.

ISSN:0041-1450    

DOI:10.1080/00411459708221788

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

This paper presents an approximate solution to the neutron transport equation by using the theory of reproducing kernels. The approximate solution can be constructed by only finite many values of a function. This method can be generalized in a tensor product space.

ISSN:0041-1450    

DOI:10.1080/00411459708221789

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

We give a complete description of the spectrum of the transport operator for a bounded convex body. We show that the Jorgen's spectra satisfy the summability: σ < ∞ where τ is the maximum escape time. Moreover, we obtain the eigenfunction expansion of the transport semigroupEt) for allt> 6τ.

ISSN:0041-1450    

DOI:10.1080/00411459708221790

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor

摘要:

U-scalar operators are discussed in this paper. We give the necessary and sufficient conditions for an operator with purely discrete spectrum to be u-scalar. And generally, we prove that a u-scalar operator is Hermitian in the sense of some topology. A new example of u-scalar operator is given. This operator is not a spectral operator of scalar type.

ISSN:0041-1450    

DOI:10.1080/00411459708221791

出版商:Taylor & Francis Group    

年代:1997

数据来源: Taylor