Geodesic
Generalized solutions to the gKdV equation
Electronic journal of differential equations, Tome 2010 (2010)
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 $s\in \mathbb{R}$.
Classification : 35D05, 35Q20
Keywords: gKdV equation, generalized solution, singular initial condition 
@article{EJDE_2010__2010__a69,
     author = {Melo,  Maurilio Marcio},
     title = {Generalized solutions to the {gKdV} equation},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1196.35186},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a69/}
}
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Melo,  Maurilio Marcio. Generalized solutions to the gKdV equation. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a69/