THE STRUCTURE OF THE FUNDAMENTAL SOLUTION OF THE TIME-INDEPENDENT TRANSPORT-EQUATION

Authors
Citation
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
Citations number
15
Categorie Soggetti
Mathematics,Mathematics,Mathematics,Mathematics
ISSN journal
0022247X
Volume
221
Issue
2
Year of publication
1998
Pages
430 - 451
Database
ISI
SICI code
0022-247X(1998)221:2<430:TSOTFS>2.0.ZU;2-Q
Abstract
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.