摘要:

For abstract kinetic equations on a half-line the albedo operator which gives the initial value as a function of the half-range boundary data, is written in terms of operator-valued generalizations of Chandrasekhar's H-functions, for which coupled non-linear equations are derived. Applications are given to transfer of polarized light, neutron transport and strong evaporation of liquids.

ISSN:0041-1450    

DOI:10.1080/00411458408214484

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

New characteristic methods for the solution of the x,y geometry discrete ordinates neutron transport equation have recently been introduced. Five polynomials, without any continuity requirement are defined on each mesh cell. A polynomial of order k is used to approximate the angular flux inside the cell, while polynomial approximations of order ℓ are used along the cell edges.

ISSN:0041-1450    

DOI:10.1080/00411458408214485

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Spectral properties of the Boltzmann operator linearized around a local Maxwellian have been investigated. We show that the spectrum is the same in all spaces LP, 1 ⩽ p ⩽ ∞, It consists of a half-plane Re λ ⩽v0and a countably many eigenvalues in a strip -v0< Re λ ⩽ 0. We analyse eigenvalues with Re λ = 0 and show that when linearization is performed around a space nonhomogeneous Maxwellian all eigenvalues lie in the open strip -λ0< Re λ < 0. For a space homogeneous Maxwellian the fivefold degenerate eigenvalue λ = 0 is the only one with Re λ = 0.

ISSN:0041-1450    

DOI:10.1080/00411458408214486

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The three sections of the paper contain the following results: 1) Theorems concerning local existence, uniqueness and nonnegativity of mild solutions for semilinear, strictly hyperbolic systems with initial values in L∞+(R3). 2) Results about the global existence of mild solutions for two examples of such systems (one example is the Carleman model) in one dimension when the initial data are in L1Loc, +(R). 3) Decay estimates for the Carleman model on the real line and for the Carleman model in a box wiht reflecting boundary condintons.

ISSN:0041-1450    

DOI:10.1080/00411458408214487

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

This paper provides a general description of reflection laws in kinetic theory including all reflection laws of interest. Solutions of the corresponding initial and boundary value problem for a collisionless gas confined in a bounded region areconstructed and analyzed. We, inaddition, provide conditions guaranteeing the uniqueness of solutions and the conservation o f mass.

ISSN:0041-1450    

DOI:10.1080/00411458408214488

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The techniques of part I and a method due t o Kaniel and Shinbrot are applied to prove a local existence theorem for the Boltzmann Equation under general boundary conditions. For a special boundary condition a global existence theorem for a hard sphere gas is proven for appropriately chosen coefficients.

ISSN:0041-1450    

DOI:10.1080/00411458408214489

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

The equations of transfer of the Boltzmann equation for Maxwellian molecules can be solved recursively. For homogeneous one-dimensional systems these equations form a system o f ordinary nonlinear differential equations. For this system the recursion is carried out explicitely using a graphtheoretical method.

ISSN:0041-1450    

DOI:10.1080/00411458408214490

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

A set of continuum and discrete eigenfunctions, derived previously for half-space transport problems with a scattering ratio that is a bilinear function of position, is examined. For a Hölder continuous angular flux incident on the half-space, this eigenfunction set is proved to be half-range complete and the expansion coefficient for the continuum eigenfunctions is proved to be a continuous function of the spectral variable Y. Also, equations for the exiting flux, which are derived using this eigenfunction set, are proved to possess a unique, analytic solution.

ISSN:0041-1450    

DOI:10.1080/00411458408214491

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

It is shown that the mechanical equivalent of heat (Joule's constant) cannot be constant out of thermodynamic equilibrium. This is the main result of the paper and is obtained in the first part. The second part is concerned with heat flow in steady state conditions. By assuming that the energy of heat flow does not depend on the properties of the medium through which the heat flow occurs, a relationship between heat flow and energy is derived.

ISSN:0041-1450    

DOI:10.1080/00411458408214492

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor

摘要:

Herbert F. Wang and Mary P. Anderson, W. H. Freeman and Co., San Francisco, 1982, viii + 237 pp., $30.95

ISSN:0041-1450    

DOI:10.1080/00411458408214493

出版商:Taylor & Francis Group    

年代:1984

数据来源: Taylor