Invariant Manifolds for Random and Stochastic Partial Differential Equations
Keyword(s):
AbstractRandom 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.
2011 ◽
Vol 52
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pp. 072702
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2003 ◽
Vol 31
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pp. 2109-2135
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2006 ◽
Vol 9
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pp. 193-221
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2018 ◽
Vol 18
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pp. 1850040
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1998 ◽
Vol 14
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pp. 883-903