The Structure of the Fundamental Solution of the Time-Independent Transport EquationU

The structure of singularities of the fundamental solution of the time-independent one-speed transport equation with smooth coefficients is studied. This structure is more complicated than in the elliptic equation case: two first terms in the decomposition have a singular support and two others are regular unbounded distributions. The exact expressions for the first two terms and estimates for the others are presented. The regular parts of these singularities contain some significant information concerning the medium and hence the exact description of these singularities may be useful in nondestructive control