UNIQUENESS PROBLEMS IN THE MATHEMATICS OF MULTIPLE SCATTERING
Abstract
Some recent mathematical studies concerning the uniqueness of solutions to Chandrasekhar's mathematical formulation of principles of invariance in the theory of radiative transfer are reported. It is shown that the X and Y equations and the psi(m) sub l and phi(m) sub l equations of Chandrasekhar have a multiplicity of solutions for many phase functions describing local scattering, the extent of this nonuniqueness having been only partially explored by Chandrasekhar. The desired solution to the X and Y equations is selected by imposing two additional linear constraints, which differ in the conservative case from those imposed by Chandrasekhar. An extension will later be made of these results to the psi(m) sub l and phi(m) sub l equations. A new formulation of all this theory is being worked out in terms of linear equations which are particularly well suited to numerical computation for thick atmospheres. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 01, 1962
- Accession Number
- AD0287114
Entities
People
- T.w. Mullikin
Organizations
- RAND Corporation