[For the entire collection see Zbl 0747.00025.]
The article is concerned with a discussion of parameter-dependent and parabolic pseudo-differential boundary value problems. First an outline of the theory of Boutet de Monvel is given and in particular the transmission condition for symbols in \(S^ d_{1,0}\) is characterized. Then the author extends the theory to parameter-dependent symbol classes, applies the theory to parabolic initial-boundary value problems, considers convenient compatibility conditions and gives a solution theory in anisotropic Sobolev spaces. Finally, as an application he considers some special examples in the fields of singular perturbation problems, control theory and Navier-Stokes operators.