Stability for Lie–Trotter products for some operator matrix semigroups

Coupled systems of linear differential equations in Banach spaces can be often handled by the theory of C 0 -semigroups of operator matrices. We study the stability of Lie–Trotter products of such matrix semigroups, and present three classes of examples (abstract delay equations, abstract inhomogeneous equations, abstract dynamic boundary value problems) and some open problems. This survey is based on the papers [1], [2] and [5], to which we refer the interested reader for more details and extensive bibliographical information.