An initial boundary-value problem in a half-strip for the Korteweg-de Vries equation in fractional-order sobolev spaces

An initial boundary-value problem in a half-strip with one boundary condition for the Korteweg-de Vries equation is considered and results on global well-posedness of this problem are established in Sobolev spaces of various orders, including fractional. Initial and boundary data satisfy natural (or close to natural) conditions, originating from properties of solutions of a corresponding initial-value problem for a linearized KdV equation. An essential part of the study is the investigation of special solutions of a "boundary potential" type for this linearized KdV equation.