On the well-posedness of a class of non-autonomous SPDEs : an operator-theoretical perspective

Picard, Rainer and Trostorff, Sascha and Waurick, Marcus (2018) On the well-posedness of a class of non-autonomous SPDEs : an operator-theoretical perspective. GAMM-Mitteilungen / GAMM-Reports. e201800014. ISSN 0936-7195

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    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 [Suß, A. & Waurick, M. A Solution Theory for a General Class of SPDEs. 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.