Algebraic-Complex Scheme for Dirichlet–Neumann Data for Parabolic System

In this paper, we use the Laplace–Laplace transformation and complex analysis to give a systematical scheme to determine the proper boundary conditions for initial-boundary value problems in the half space and to construct exponentially sharp pointwise structures of the boundary data. Here, we have used the boundary value problems with the Robin boundary conditions for the convection heat equations and the linearized compressible Navier–Stokes equation with a constant convection velocity to demonstrate this scheme.