Initial-Boundary Value Problems of Fokas’ Transform Method

A new, uni?ed transform method for boundary value problems on linear and integrable nonlinear partial di?erential equations was recently intro- duced by Fokas. We consider initial boundary value problems for linear, constant- coe?cient evolution equations of arbitrary order on a ?nite domain. We use Fokas’ method to fully characterize well-posed problems. We derive an implicit solution to the IBVP. We also discuss the global relation and classi?cation of boundary condition.