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 (https://doi.org/10.1002/gamm.201800014)

[thumbnail of Picard-etal-GAMM-Reports-2018-On-the-well-posedness-of-a-class-of-non-autonomous-SPDEs]
Preview
 Text. Filename: Picard_etal_GAMM_Reports_2018_On_the_well_posedness_of_a_class_of_non_autonomous_SPDEs.pdf
Accepted Author Manuscript
Download (289kB)| Preview

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.

ORCID iDs

Picard, Rainer, Trostorff, Sascha and Waurick, Marcus ORCID logoORCID: https://orcid.org/0000-0003-4498-3574;
CORE (COnnecting REpositories)