On an initial boundary value problem in a bounded domain for the generalized Korteweg-de Vries equation

The author establishes the nonlocal solvability, stability and well-posedness of an initial-boundary value problem in a rectangle for a class of generalized KdV equations. Slobodetskiĭ spaces are introduced, and the standard contraction mapping argument is used to establish the local existence in time of a generalized solution. Finally an a priori estimate is derived to continue globally in time a local generalized solution.