Non-random Invariant Sets for Some Systems of Parabolic Stochastic Partial Differential Equations

2004 ◽  
Vol 22 (6) ◽  
pp. 1421-1486 ◽  
Author(s):  
I. D. Chueshov ◽  
P.-A. Vuillermot
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Invariant Sets ◽  
Partial Differential

On smooth approximation for random attractor of stochastic partial differential equations with multiplicative noise

2018 ◽  
Vol 18 (05) ◽  
pp. 1850040 ◽  
Author(s):  
Hongbo Fu ◽  
Xianming Liu ◽  
Jicheng Liu ◽  
Xiangjun Wang
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Stochastic Partial Differential Equations ◽  
Random Attractor ◽  
Invariant Sets ◽  
Stochastic Pdes ◽  
Polygonal Approximation ◽  
Smooth Approximation ◽  
Partial Differential ◽  
Random Partial Differential Equations

Wong–Zakai type approximation for stochastic partial differential equations (abbreviate as PDEs) is well studied. Besides the polygonal approximation, a type of smooth noise approximation is considered. After showing the existence of random attractor for a class of random partial differential equations defined on the entire space [Formula: see text], when random color noises tend to white noise, the solutions and invariant sets between original stochastic PDEs and random PDEs are compared. Some continuity results of random attractor in random dynamical systems are indicated.

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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