Generalized Function Algebras and PDEs with Singularities. A Survey.

Marko Nedeljkov, Stevan Pilipović

The aim of this survey article is to explain basic ideas of generalized function algebras (Part I), to illustrate the analysis of second order PDEs (Part 11) and first order hyperbolic systems (Part Ill) with singular coefficients and singular data. Part I deals with the basic definitions of Colombeau type spaces and algebras, while Parts 11 and III present main statements of our investigations on PDEs of quoted types. Especially, complete proofs on solving elliptic linear equations with singular coefficients and singular data are given.