摘要:

Let (Ω, μ) be a measure space. A bounded operator A on L1(μ) is calledsubstochasticif A ≥ 0 and ‖A‖ ≤ 1. It is calledstochasticif additionally ‖Af‖ = ‖f‖ for all f ε L1(μ)+.

ISSN:0041-1450    

DOI:10.1080/00411458708204302

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We give a complete description of therealpoint spectrum of the transport operator for positive collision operators: necessary and sufficient conditions for existence; necessary and sufficient conditions for finiteness; estimates of the number of eigenvalues; localization of the point spectrum. Finally we indicate some open problems.

ISSN:0041-1450    

DOI:10.1080/00411458708204303

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

Wesurvey the recent results on the scattering theory for transport equation in whole space and improve some results of our previous paper [2] on this topic.

ISSN:0041-1450    

DOI:10.1080/00411458708204304

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

A review is given of integral formulations of a variety of boundary value problems in abstract kinetic theory. Apart from the introduction of the boundary value problems and their equivalent integral formulations, we pay special attention to their most important applications. In the first place we shall discuss representations of solutions in generalized H-, X- and Y-functions. In the second place we shall develop the projection and semigroup formalism using only the integral formulation and not using selfadjointness of the scattering operators. In the third place we shall discuss the impact of the equivalence theory in combination with the Fredholm alternative on the existence and uniqueness theory. We conclude this work with a discussion of methods of proving existence and uniqueness of solutions of stationary transport equations.

ISSN:0041-1450    

DOI:10.1080/00411458708204305

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We describe a method based on energy estimates for the study of the half space milne problem. To show the range of application of the method we start from the linear transport equation and we consider other problems (Including some short summaries of results described in companion papers). On the other hand, we do not consider classical or more explicit methods, which where introduced already long time ago. (cf. E. Hopf [17], or I. Busbrldge [18]).

ISSN:0041-1450    

DOI:10.1080/00411458708204306

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

We study a simplified model of the Fokker-Planck equation of plasma physics. This model only involves a linear angular diffusion for a monoenergetic beam. We discuss the problem of existence and uniqueness of solutions in both the evolution and the stationary cases; Then we justify the diffusion approximation, with either the Dirichlet, or the Robin boundary conditions. For that purpose, we are led to give some results on the Milne problem and to compute the extrapolation length.

ISSN:0041-1450    

DOI:10.1080/00411458708204307

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

In this paper, we recall some results on the radiative transfer equations:

ISSN:0041-1450    

DOI:10.1080/00411458708204308

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

When the mean free path of the photons are small the radiative transfer equation may be approximated by a non linear diffusion equation. In order to find the right boundary condition for this last equation it is necessary to solve a non linear frequency dependent transport equation in a half space. This non linear half space problem is first studied. Afterwards a linearized half space problem is considered and the limit of the solution is calculated using Chandrasekhar's techniques.

ISSN:0041-1450    

DOI:10.1080/00411458708204309

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The Hilbert and Chapman-Enskog expansions approximate solutions of the Boltzmann equation, but each has some disadvantages: The Hilbert expansion, which results in nonlinear and linearized Euler equations, is invalid for weak shocks, weak boundary layers and long time asymptotics. The Chapman-Enskog expansion results in nonlinear Euler then Navier-Stokes then Burnett and super-Burnett equations. Navier-Stokes is correct for weak shocks, weak boundary layers and long time asymptotics, but the Burnett equations have spurious high order dispersive effects. In this paper a modified expansion is developed, which combines the best features of the two expansions. It results in nonlinear and linearized Navier-Stokes equations only and is valid in the above-mentioned regimes.

ISSN:0041-1450    

DOI:10.1080/00411458708204310

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor

摘要:

The inviscid equations for compressible flows predict the occurence of singularities after a finite time for a large class of smooth initial data[1]. Based upon the hyperbolic nature of these equations, the method of characteristics allows a detailed study of this phenomenon in one spatial dimension. Qualitatively speaking, the formation of discontinuities is related to the fact that perturbations with a larger amplitude move faster and pile up on lower amplitude perturbations. Thus, smooth initial data may produce after a finite time infinitely sharp density and/or velocity variations. This violates a basic assumptions of continuous hydrodynamics: any field as the mass density or the fluid velocity must be almost constant on molecular scales, that is on a mean free path in gases which I shall consider from now on.

ISSN:0041-1450    

DOI:10.1080/00411458708204311

出版商:Taylor & Francis Group    

年代:1987

数据来源: Taylor