Kinks in a Stochastic PDE

2003 ◽  
pp. 435-443 ◽  
Author(s):  
Grant Lythe ◽  
Salman Habib
Keyword(s):  
Stochastic Pde

Random attractors for 3D Benjamin–Bona–Mahony equations derived by a Laplace-multiplier noise

2017 ◽  
Vol 18 (01) ◽  
pp. 1850004 ◽  
Author(s):  
Yangrong Li ◽  
Renhai Wang
Keyword(s):  
Dynamical System ◽  
Multiplicative Noise ◽  
Careful Analysis ◽  
Random Dynamical System ◽  
Stochastic Pde ◽  
Limit Set ◽  
Cutoff Function ◽  
Random System ◽  
Random Attractors ◽  
Bbm Equation

This paper contributes the dynamics for stochastic Benjamin–Bona–Mahony (BBM) equations on an unbounded 3D-channel with a multiplicative noise. An interesting feature is that the noise has a Laplace-operator multiplier, which seems not to appear in any literature for the study of stochastic PDE. After translating the stochastic BBM equation into a random equation and deducing a random dynamical system, we obtain both existence and semi-continuity of random attractors for this random system in the Sobolev space. The convergence of the system can be verified without the lower bound assumption of the nonlinear derivative. The tail-estimate is achieved by using a square of the usual cutoff function and by a careful analysis of the solution’s biquadrate. A spectrum method is also applied to prove the collective limit-set compactness.

Smoothed aggregation algebraic multigrid for stochastic PDE problems with layered materials

2014 ◽  
Vol 21 (2) ◽  
pp. 239-255 ◽  
Author(s):  
Marian Brezina ◽  
Alireza Doostan ◽  
Tom Manteuffel ◽  
Steve McCormick ◽  
John Ruge
Keyword(s):  
Layered Materials ◽  
Algebraic Multigrid ◽  
Stochastic Pde ◽  
Smoothed Aggregation

scholarly journals Large deviations for stochastic PDE with Lévy noise

2011 ◽  
Vol 260 (3) ◽  
pp. 674-723 ◽  
Author(s):  
Andrzej Święch ◽  
Jerzy Zabczyk
Keyword(s):  
Large Deviations ◽  
Lévy Noise ◽  
Stochastic Pde ◽  
Levy Noise

scholarly journals Glauber dynamics of 2D Kac–Blume–Capel model and their stochastic PDE limits

2018 ◽  
Vol 275 (6) ◽  
pp. 1321-1367 ◽  
Author(s):  
Hao Shen ◽  
Hendrik Weber
Keyword(s):  
Glauber Dynamics ◽  
Stochastic Pde
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