Matheus Cheque Bortolan

3.1 Well-Posedness of the Problem In order to obtain existence, uniqueness and continuity with respect to initial data for (W–Eq), we first present some estimates related to the functions f $$ f $$ and F $$ F $$ defined in 1 and 1. The proof of the next result is standard, and can be found in detail, for instance, in [17]. Proposition 3.1.For all u , v ∈ ℝ $$ u,v\in \mathbb{R} $$ , we have i.