(WEAKLY) 3-DIMENSIONAL CASEOLOGY

The singular eigenfunction technique of Case for solving one-dimension al planar symmetry linear transport problems is extended to a restrict ed class of three-dimensional problems. This class involves planar geo metry, but with forcing terms (either boundary conditions or internal sources) which are weakly dependent upon the transverse spatial variab les. Our analysis involves a singular perturbation about the classic p lanar analysis, and leads to the usual Case discrete and continuum mod es, but modulated by weakly dependent three-dimensional spatial functi ons. These functions satisfy parabolic differential equations, with a different diffusion coefficient for each mode. Representative one-spee d time-independent transport problems are solved in terms of these gen eralized Case eigenfunctions. Our treatment is very heuristic, but may provide an impetus for more rigorous analysis.