Generalized Dirichlet to Neumann Maps for Linear Dispersive Equations on   Half-Line
  A large class of initial-boundary value problems of linear evolution partial differential equations formulated on the half-line is analyzed via the unified transform method. In particular, explicit formulae are presented for the generalized Dirichlet to Neumann maps. Namely, the determination of the unknown boundary values in terms of an essential set of given data. 
Athanassios S. Fokas and Zipeng Wang
math.AP