On the well‐posedness of a class of nonautonomous SPDEs: An operator‐theoretical perspective. Issue 4 (12th October 2018)

• Record Type: Journal Article
• Authors: Picard, Rainer; Trostorff, Sascha; Waurick, Marcus
• Other Names: Jacob Birgit guestEditor.; Behrndt Jussi guestEditor.; Tretter Christiane guestEditor.; Trunk Carsten guestEditor.
• Is Part Of: Mitteilungen der Gesellschaft für Angewandte Mathematik und Mechanik. Volume 41:Issue 4(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-10-12
• Subjects: differential inclusions -- evolutionary equations -- nonautonomous equations -- nonlinear equations -- stochastic equations of mathematical physics -- stochastic partial differential equations -- weak solutions; Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; 510.5
• DOI: 10.1002/gamm.201800014
• Languages: English
• ISSNs: 0936-7195

Abstract

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.