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

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