Well and ill-posed problems for the KdV and Kawahara equations - doi: 10.5269/bspm.v26i1-2.7419

Abstract

Well and ill-posedness of initial-boundary value problems for the KdV and Kawahara equations posed on a nite 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.