Positive solution of a time and energy dependent neutron transport problem

Journal Article · Wed Jan 01 04:00:00 EST 1975 · Journal of Mathematical Physics

DOI:https://doi.org/10.1063/1.522451· OSTI ID:4186853

Pao, C. V.

A constructive method is given for the determination of a solution and an existence--uniqueness theorem for some nonlinear time and energy dependent neutron transport problems, including the linear transport system. The geometry of the medium under consideration is allowed to be either bounded or unbounded which includes the geometry of a finite or infinite cylinder, a half-space and the whole space R/subm/ (m=1,2,center-dotcenter-dotcenter-dot). Our approach to the problem is by successive approximation which leads to various recursion formulas for the approximations in terms of explicit integrations. It is shown under some Lipschitz conditions on the nonlinear functions, which describe the process of neutrons absorption, fission, and scattering, that the sequence of approximations converges to a unique positive solution. Since these conditions are satisfied by the linear transport equation, all the results for the nonlinear system are valid for the linear transport problem. In the general nonlinear problem, the existence of both local and global solutions are discussed, and an iterative process for the construction of the solution is given.

• Research Organization: Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27607
• Sponsoring Organization: USDOE
• NSA Number: NSA-33-002074
• OSTI ID: 4186853
• Journal Information: Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 10 Vol. 16; ISSN JMAPAQ; ISSN 0022-2488
• Publisher: American Institute of Physics (AIP)
• Country of Publication: United States
• Language: English

Related Subjects

*NEUTRON TRANSPORT THEORY-- ITERATIVE METHODS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUNDARY CONDITIONS
ENERGY DEPENDENCE
NONLINEAR PROBLEMS
PERTURBATION THEORY
SERIES EXPANSION
TIME DEPENDENCE