Mathematical problems in kinetic transport theory

Some problems in mathematical transport theory are examined with emphasis on the spherical harmonics method. Attention is given to the convergence of the spherical harmonics method, statement of boundary conditions, and types and properties of solutions to equations of sperical harmonics in the vicinity of corner points and points of junction between discontinuity lines. A variational principle is demonstrated for the general case using a PN-approximation. New efficient methods for solving the linearized Boltzmann equation are proposed and analyzed.