Stable Manifold Theorem for Semilinear Stochastic Evolution Equations and Stochastic Partial Differential Equations.

Intro -- Contents -- Introduction -- Part 1. The stochastic semiflow -- 1.1 Basic concepts -- 1.2 Flows and cocycles of semilinear see's -- (a) Linear see's -- (b) Semilinear see's -- 1.3 Semilinear spde's: Lipschitz nonlinearity -- 1.4 Semilinear spde's: Non- Lipschitz nonlinearity -- (a) Stochastic reaction diffusion equations -- (b) Burgers equation with additive noise -- Part 2. Existence of stable and unstable manifolds -- 2.1 Hyperbolicity of a stationary trajectory -- 2.2 The nonlinear ergodic theorem -- 2.3 Proof of the local stable manifold theorem -- 2.4 The local stable manifold theorem for see's and spde's -- (a) See's: Additive noise -- (b) Semilinear see's: Linear noise -- (c) Semilinear parabolic spde's: Lipschitz nonlinearity -- (d) Stochastic reaction diffusion equations: Dissipative nonlinearity -- (e) Stochastic Burgers equation: Additive noise -- Acknowledgments -- Bibliography.

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Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.