Random attractor for a stochastic damped wave equation with multiplicative noise on unbounded domains

2011 ◽  
Vol 12 (6) ◽  
pp. 3468-3482 ◽  
Author(s):  
Zhaojuan Wang ◽  
Shengfan Zhou ◽  
Anhui Gu
Keyword(s):  
Wave Equation ◽  
Multiplicative Noise ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Damped Wave Equation

scholarly journals Exponential decay for the damped wave equation in unbounded domains

2016 ◽  
Vol 18 (06) ◽  
pp. 1650012 ◽  
Author(s):  
Nicolas Burq ◽  
Romain Joly
Keyword(s):  
Wave Equation ◽  
Initial Data ◽  
Exponential Decay ◽  
Unbounded Domain ◽  
Unbounded Domains ◽  
Geometric Control ◽  
Damped Wave Equation ◽  
Logarithmic Decay ◽  
And Control

We study the decay of the semigroup generated by the damped wave equation in an unbounded domain. We first prove under the natural geometric control condition the exponential decay of the semigroup. Then we prove under a weaker condition the logarithmic decay of the solutions (assuming that the initial data are smoother). As corollaries, we obtain several extensions of previous results of stabilization and control.

Dynamic behavior of stochastic p-Laplacian-type lattice equations

2016 ◽  
Vol 17 (05) ◽  
pp. 1750040 ◽  
Author(s):  
Anhui Gu ◽  
Yangrong Li
Keyword(s):  
Dynamic Behavior ◽  
Multiplicative Noise ◽  
Finite Lattice ◽  
Unbounded Domains ◽  
Random Attractor ◽  
Infinite Lattice ◽  
Lower Semi ◽  
The Family ◽  
Random Attractors ◽  
Type Lattice

In this paper, we consider the dynamic behavior of stochastic [Formula: see text]-Laplacian-type lattice equations perturbed by a multiplicative noise. Under weaker dissipative conditions compared to the cases of stochastic [Formula: see text]-Laplacian-type equations in bounded and unbounded domains, we first obtain the existence of a unique random attractor. We also establish the approximation of the random attractors from finite lattice to infinite lattice, which indicates that the family of random attractors is upper and lower semi-continuous when the number of the lattice nodes tends to infinity.

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