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.
Keywords and Phrases
Unified Transform Method, Nonlinear Partial Differential Equations, IBVP.
A.M.S. subject classiﬁcation