Elementary solutions of the transport equation and their applications

A new method of treating problems involving the transport equation is discussed. Starting from Van Kampen's observation that it is sufficient that "solutions" be distributions, the elementary solutions of the homogeneous equation are considered. These are found to have completeness and, in some cases, orthogonality properties which lead to the solution of more interesting problems by a conventional eigenfunction expansion. While the method is illustrated here with the simplest examples of neutron diffusion, it seems to be generally applicable.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/32430/1/0000511.pd