Existence and uniqueness of solutions to stochastic functional differential equations in infinite dimensions. (September 2015)

• Record Type: Journal Article
• Authors: Röckner, Michael; Zhu, Rongchan; Zhu, Xiangchan
• Is Part Of: Nonlinear analysis. Volume 125(2015)
• Page Start: 358
• Page End: 397
• Publication Date: 2015-09
• Subjects: 60H15 -- 60H30 -- 35R60; Stochastic functional equation -- Stochastic partial differential equations with delay -- Martingale problem -- Local monotonicity; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.05.019
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: In this paper, we present a general framework for solving stochastic functional differential equations in infinite dimensions in the sense of martingale solutions, which can be applied to a large class of SPDE with finite delays, e.g. d -dimensional stochastic fractional Navier–Stokes equations with delays, d -dimensional stochastic reaction–diffusion equations with delays, d -dimensional stochastic porous media equations with delays. Moreover, under local monotonicity conditions for the nonlinear terms we obtain the existence and uniqueness of strong solutions to SPDE with delays.