On P_N Interface and Boundary Conditions

We investigate the degeneracy of the first-order P_N equations and construct interface and boundary conditions that ensure a unique solution. Our technique is based on establishing an equivalence between the first- and second-order P_N equations and showing that the (regular) second-order equations with opposite parity to N are nondegenerate. Assuming bounded angular flux moments and sources, we derive interface and boundary conditions for the regular second-order equations that, via the equivalence, are those to be used with the first-order P_N equations. While providing independent derivations, our results reproduce those derived using solid harmonic expansions by Davison and Rumyantsev in the 1950s.