Electron. J. Diff. Equ., Vol. 2012 (2012), No. 87, pp. 1-20.

Generalized Heaviside functions in the Colombeau theory context

Francisco Villarreal

We defined generalized Heaviside functions for a variable x in $\mathbb{R}^n$, and for variables (x,t) in $\mathbb{R}^n\times\mathbb{R}^m$. Then study properties such as: composition, invertibility, and association relation (the weak equality). This work is developed in the Colombeau generalized functions context.

Submitted November 1, 2011. Published June 4, 2012.
Math Subject Classifications: 46F30, 35G20.
Key Words: Generalized function; Heaviside function; distribution.

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Francisco Villarreal
Departamento de Matemática, FEIS-UNESP
15385-000, Ilha Solteira, S&atilce;o Pãulo, Brazil
email: villa@mat.feis.unesp.br

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