An. Bondarenko, THE STRUCTURE OF THE FUNDAMENTAL SOLUTION OF THE TIME-INDEPENDENT TRANSPORT-EQUATION, Journal of mathematical analysis and applications, 221(2), 1998, pp. 430-451
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 equat
ion case: two first terms in the decomposition have a singular support
and two others are regular unbounded distributions. The exact express
ions for the first two terms and estimates for the others are presente
d, The regular parts of these singularities contain some significant i
nformation concerning the medium and hence the exact description of th
ese singularities may be useful in nondestructive control, (C) 1998 Ac
ademic Press.