Approximation of Smooth Stable Invariant Manifolds for Stochastic Partial Differential Equations

2019 ◽  
Vol 32 (2) ◽  
pp. 112-128
Author(s):  
Zhongkai Guo sci
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Invariant Manifolds ◽  
Partial Differential ◽  
Stable Invariant Manifolds ◽  
Stable Invariant

scholarly journals Invariant manifolds for stochastic partial differential equations

2003 ◽  
Vol 31 (4) ◽  
pp. 2109-2135 ◽  
Author(s):  
Bj�rn Schmalfuss ◽  
Kening Lu ◽  
Jinqiao Duan
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Invariant Manifolds ◽  
Partial Differential

scholarly journals Invariant Manifolds for Random and Stochastic Partial Differential Equations

2010 ◽  
Vol 10 (1) ◽  
Author(s):  
Tomás Caraballo ◽  
Jinqiao Duany ◽  
Kening Lu ◽  
Björn Schmalfuβ
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Invariant Manifolds ◽  
Complex Dynamics ◽  
Nonuniform Hyperbolicity ◽  
Partial Differential ◽  
Random Partial Differential Equations ◽  
Manifold Theory ◽  
Stochastic Ordinary Differential Equations

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.

scholarly journals Existence of weak solutions to SPDEs with fractional Laplacian and non-Lipschitz coefficients

2021 ◽  
Author(s):  
Shohei Nakajima
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Weak Solutions ◽  
Stochastic Partial Differential Equations ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Partial Differential ◽  
Continuity Theorem ◽  
Existence Of Weak Solutions ◽  
One Dimensional

AbstractWe prove existence of solutions and its properties for a one-dimensional stochastic partial differential equations with fractional Laplacian and non-Lipschitz coefficients. The method of proof is eatablished by Kolmogorov’s continuity theorem and tightness arguments.

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