Fundamental matrix of the Hilbert problem in transport theory

Journal Article · Mon Jan 01 00:00:00 EST 1973 · Transp. Theory Stat. Phys.; (United States)

DOI:https://doi.org/10.1080/00411457308247936· OSTI ID:7263021

Rajamaki, M

A method of solving the homogeneous Hilbert problem encountered in the two-media case of the one-dimensional transport equation with degenerate scattering kernels is developed. The existence of the corresponding fundamental matrix is proved when the fundamental matrices for both the full-range problems exist and the elements of these matrices and of their inverses belong to a class L/sub p/, p greater than 2, and the zeroes of the dispersion functions are of integer order. Matrices related to the fundamental matrices satisfy a Fredholm equation whose free term involves unknown polynomial elements. Means of constructing the fundamental matrix from certain solutions of this equation are investigated. Sufficient supplementary conditions are presented in the form of an algebraic equation. Since the kernel is simple in form and its norm approaches zero with the cross sections of both media approaching each other, the Fredholm equation is very suitable for computation.

• Research Organization: Helsinki Univ. of Technology, Otaniemi, Finland
• OSTI ID: 7263021
• Journal Information: Transp. Theory Stat. Phys.; (United States), Vol. 3:4
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
TRANSPORT THEORY
MATRICES
ANALYTICAL SOLUTION
ENERGY DEPENDENCE
FREDHOLM EQUATION
HILBERT SPACE
KERNELS
ONE-DIMENSIONAL CALCULATIONS
SCATTERING
BANACH SPACE
EQUATIONS
INTEGRAL EQUATIONS
MATHEMATICAL SPACE
SPACE
657000* - Theoretical & Mathematical Physics
654003 - Radiation & Shielding Physics- Neutron Interactions with Matter
654001 - Radiation & Shielding Physics- Radiation Physics
Shielding Calculations & Experiments