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We further elaborate on the solvability of stochastic partial differentialequations (SPDEs). We shall discuss non-autonomous partial differentialequations with an abstract realization of the stochastic integral on theright-hand side. Our approach allows the treatment of equations with mixedtype, where classical solution strategies fail to work. The approach extendsprior observations in [S\"u\ss, A. \& Waurick, M. A Solution Theory for aGeneral Class of SPDEs. \emph{Stochastics and Partial Differential Equations:Analysis and Computations}, 2017, 5, 278-318], where the respective resultswere obtained for linear autonomous equations and (multiplicative) white noise.

On the Well-posedness of a Class of Non-Autonomous SPDEs: An Operator-Theoretical Perspective