Special Session 21: Evolution Equations and Integrable Systems

The well-posedness of a KdV system on the half-line

Fangchi Yan
Virginia Tech
Co-Author(s):    Alex Himonas
Using the Fokas unified transform method the well-posedness of the initial-boundary value problem of a system of KdV type equations on the half-line is studied for initial data in spatial Sobolev spaces and boundary data in the temporal Sobolev spaces suggested by the time regularity of the Cauchy problem for the corresponding linear system. First, linear estimates in Bourgain spaces are derived by utilizing the Fokas solution formula of the corresponding forced linear system. Then, using these and the needed bilinear estimates, it is shown that the iteration map defined by the Fokas solution formula is a contraction in an appropriate solution space. This talk is based on a joint work with Alex Himonas.