  We provide certain compatibility conditions for m-accretive operators such
that the adjoint of the sum is given by the closure of the sum of the
respective adjoint. We revisit the proof of well-posedness of the abstract
class of partial differential-algebraic equations known as evolutionary
equations. We show that the general mechanism provided here can be applied to
establish well-posedness for non-autonomous evolutionary equations with
$L_{\infty}$-coefficients thus not only generalising known results but opening
up new directions other methods such as evolution families have a hard time to
come by.
