Adjoints of sums of m-accretive operators and applications to non-autonomous evolutionary equations

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 $L_{\mathrm{\infty }}$-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.