Electronic Journal of Differential Equations,
Vol. 2010(2010), No. 108, pp. 1-10.
Title: Generalized solutions to the gKdV equation
Author: Maurilio Marcio Melo (Univ. Federalde Goias, Goiania, Brazil)
Abstract:
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 05, 2010.
Math Subject Classifications: 35D05, 35Q20.
Key Words: gKdV equation; generalized solution; singular initial condition