  We study an abstract class of autonomous differential inclusions in Hilbert
spaces and show the well-posedness and causality, by establishing the operators
involved as maximal monotone operators in time and space. Then the proof of the
well-posedness relies on a well-known perturbation result for maximal monotone
operators. Moreover, we show that certain types of nonlinear boundary value
problems are covered by this class of inclusions and we derive necessary
conditions on the operators on the boundary in order to apply the solution
theory. We exemplify our findings by two examples.
