Electron. J. Diff. Equ., Vol. 2010(2010), No. 108, pp. 1-10.

Generalized solutions to the gKdV equation

Maurilio Marcio Melo

In this article we study the Cauchy problem in $\mathcal{G}_2((0,T)\times \mathbb{R})$ (the algebra of generalized functions, in the sense of Colombeau) for the generalized Korteweg-de Vries equation, with initial condition $\varphi \in \mathcal{G}_2(\mathbb{R)}$, which contains $H^s(\mathbb{R})$, for $s\in \mathbb{R}$.

Submitted October 16, 2009. Published August 5, 2010.
Math Subject Classifications: 35D05, 35Q20.
Key Words: gKdV equation; generalized solution; singular initial condition

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Maurílio Márcio Melo
Instituto de Matemática e Estatística
Universidade Federalde Goiás
Caixa Postal 131, 74001-970 - Goiânia, Brazil
email: melo@mat.ufg.br

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