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

Abstract

We further elaborate on the solvability of stochastic partial differential equations (SPDEs). We shall discuss non-autonomous partial differential equations with an abstract realization of the stochastic integral on the right-hand side. Our approach allows the treatment of equations with mixed type, where classical solution strategies fail to work. The approach extends prior observations in [Süß, A. \& Waurick, M. A Solution Theory for a General Class of SPDEs. \emph{Stochastics and Partial Differential Equations: Analysis and Computations}, 2017, 5, 278-318], where the respective results were obtained for linear autonomous equations and (multiplicative) white noise.

20 pages; referee's comments incorporated; to appear in GAMM-Mitteilungen