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

Rainer Picard, Sascha Trostorff, Marcus Waurick

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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.
Original languageEnglish
Article numbere201800014
Number of pages16
JournalGAMM-Mitteilungen / GAMM-Reports
Early online date12 Oct 2018
DOIs
Publication statusE-pub ahead of print - 12 Oct 2018

Keywords

  • stochastic partial differential equations
  • evolutionary equations
  • stochastic equations of mathematical physics
  • weak solutions
  • non-autonomous equations
  • nonlinear equations
  • differential inclusions

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