On the well‐posedness of a class of nonautonomous SPDEs: An operator‐theoretical perspective

Abstract

We further elaborate on the solvability of stochastic partial differential equations (SPDEs). We shall discuss nonautonomous 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 a previous study, where the respective results were obtained for linear autonomous equations and (multiplicative) white noise.

Homogenisation and the weak operator topology

“…[20]. For an extension to stochastic evolutionary equations we refer to [24] (autonomous case) and [21] (non-autonomous case).…”