Invariant Manifolds for Random and Stochastic Partial Differential Equations

By Tomás Caraballo, Jinqiao Duany, Kening Lu, B. Schmalfuβ. 2009

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Abstract Random invariant manifolds are geometric objects useful for understanding complex dynamics under stochastic infuences. Under a nonuniform hyperbolicity or a nonuniform exponential dichotomy condition, the existence of random pseudo- stable and pseudo-unstable manifolds for a class of random partial differential equations and stochastic partial differential equations is shown. Unlike the in- variant manifold theory for stochastic ordinary differential equations, random norms are not used. The result is then applied to a nonlinear stochastic partial differential equation with linear multiplicative noise.

Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/1ba939edd86abfd1d4b1c4cc992047b38bc5ff04