Wong–Zakai Approximations and Long Term Behavior of Stochastic Partial Differential Equations

2017 ◽  
Vol 31 (3) ◽  
pp. 1341-1371 ◽  
Author(s):  
Kening Lu ◽  
Bixiang Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Partial Differential ◽  
Long Term Behavior

INVARIANT FOLIATIONS FOR STOCHASTIC PARTIAL DIFFERENTIAL EQUATIONS

2008 ◽  
Vol 08 (03) ◽  
pp. 505-518 ◽  
Author(s):  
KENING LU ◽  
BJÖRN SCHMALFUß
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
White Noise ◽  
Stochastic Partial Differential Equations ◽  
Partial Differential ◽  
Invariant Foliation ◽  
All Solutions ◽  
Multiplicative White Noise ◽  
Long Term Behavior

In this paper, we study the existence of an invariant foliation for a class of stochastic partial differential equations with a multiplicative white noise. This invariant foliation is used to trace the long term behavior of all solutions of these equations.

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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