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Zeitschrift für Analysis und ihre Anwendungen

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Volume 25, Issue 4, 2006, pp. 467–477
DOI: 10.4171/ZAA/1302

Published online: 2006-12-31

Colombeau Generalized Functions and Solvability of Differential Operators

Khaled Benmeriem and Chikh Bouzar

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.

Keywords: Colombeau generalized functions, regularized derivatives, Mizohata type operators, solvability of differential operators

Benmeriem Khaled, Bouzar Chikh: Colombeau Generalized Functions and Solvability of Differential Operators. Z. Anal. Anwend. 25 (2006), 467-477. doi: 10.4171/ZAA/1302