The Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations I: The Stochastic Semiflow

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dc.creatorMohammed, Salah-Eldin A
dc.creatorZhang, Tusheng
dc.creatorZhao, Huaizhong
dc.date2005-03-16
dc.date.accessioned2026-07-07T10:03:48Z
dc.date.available2026-07-07T10:03:48Z
dc.descriptionThe main objective of this work is to characterize the pathwise local structure of solutions of semilinear stochastic evolution equations (see's) and stochastic partial differential equations (spde's) near stationary solutions. Such characterization is realized through the long-term behavior of the solution field near stationary points. The analysis falls in two parts I, II. In Part I (this paper), we prove a general existence and compactness theorem for $C^k$-cocycles of semilinear see's and spde's. Our results cover a large class of semilinear see's as well as certain semilinear spde's with non-Lipschitz terms such as stochastic reaction diffusion equations and the stochastic Burgers equation with additive infinite-dimensional noise. In Part II of this work ([M-Z-Z]), we establish a local stable manifold theorem for non-linear see's and spde's.
dc.description65 pages, 1 figure
dc.identifierhttps://arxiv.org/abs/math/0503320
dc.identifierhttp://arxiv.org/abs/math/0503320
dc.identifierMemoirs of the American Mathematical Society, Vol.196 (2008), No. 917, pp.1-105.
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/169427
dc.subjectProbability
dc.subjectDynamical Systems
dc.subject60H10; 60H20; 60H25
dc.titleThe Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations I: The Stochastic Semiflow
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