JournalszaaVol. 25, No. 4pp. 467–477

Colombeau Generalized Functions and Solvability of Differential Operators

  • Khaled Benmeriem

    Centre Universitaire de Mascara, Algeria
  • Chikh Bouzar

    University of Oran, Essenia, Algeria
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Abstract

The aim of this paper is to prove that the well known non solvable Mizohata type partial differential equations have Colombeau generalized solutions which are distributions if and only if they are solvable in the space of Schwartz distributions. Therefore the Colombeau generalized solvability includes both a new solution concept and new mathematical objects as solutions.

Cite this article

Khaled Benmeriem, Chikh Bouzar, Colombeau Generalized Functions and Solvability of Differential Operators. Z. Anal. Anwend. 25 (2006), no. 4, pp. 467–477

DOI 10.4171/ZAA/1302