Well and ill-posed problems for the KdV and Kawahara equations

Abstract

Well and ill-posedness of initial-boundary value problems for the KdV and Kawahara equations posed on a finite interval are discussed. Non-existence of solutions to ill-posed problem for the KdV equation is proved as well as solvability, uniqueness, exponential decay and asymptotics of regular solutions to the Kawahara equation subject to reasonable boundary conditions. © SPM.