scholarly journals Stability and random attractors for a reaction-diffusion equation with multiplicative noise

2000 ◽  
Vol 6 (4) ◽  
pp. 875-892 ◽  
Author(s):  
Tomás Caraballo ◽  
◽  
José A. Langa ◽  
James C. Robinson ◽  
Keyword(s):  
Diffusion Equation ◽  
Multiplicative Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Random Attractors

scholarly journals Random attractors for semilinear reaction-diffusion equation with distribution derivatives and multiplicative noise on \(\mathbb{R}^{n}\)

2020 ◽  
Vol 4 (1) ◽  
pp. 126-141
Author(s):  
Fadlallah Mustafa Mosa ◽  
◽  
Abdelmajid Ali Dafallah ◽  
Eshag Mohamed Ahmed ◽  
Mohamed Y. A Bakhet ◽  
...  
Keyword(s):  
Diffusion Equation ◽  
Multiplicative Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Random Attractors

scholarly journals Random uniform exponential attractor for stochastic non-autonomous reaction-diffusion equation with multiplicative noise in ℝ3

2019 ◽  
Vol 17 (1) ◽  
pp. 1411-1434
Author(s):  
Zongfei Han ◽  
Shengfan Zhou
Keyword(s):  
Dynamical System ◽  
Diffusion Equation ◽  
External Force ◽  
Multiplicative Noise ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Random Dynamical System ◽  
Exponential Attractor

Abstract We first introduce the concept of the random uniform exponential attractor for a jointly continuous non-autonomous random dynamical system (NRDS) and give a theorem on the existence of the random uniform exponential attractor for a jointly continuous NRDS. Then we study the existence of the random uniform exponential attractor for reaction-diffusion equation with quasi-periodic external force and multiplicative noise in ℝ3.

scholarly journals Regularity of random attractors for stochastic reaction-diffusion equations on unbounded domains

2015 ◽  
Vol 16 (01) ◽  
pp. 1650006 ◽  
Author(s):  
Bao Quoc Tang
Keyword(s):  
Diffusion Equation ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Time Dependent ◽  
Diffusion Equations ◽  
Reaction Diffusion Equation ◽  
Random Attractors ◽  
External Forces ◽  
Stochastic Reaction

The existence of a unique random attractors in [Formula: see text] for a stochastic reaction-diffusion equation with time-dependent external forces is proved. Due to the presence of both random and non-autonomous deterministic terms, we use a new theory of random attractors which is introduced in [B. Wang, J. Differential Equations 253 (2012) 1544–1583] instead of the usual one. The asymptotic compactness of solutions in [Formula: see text] is established by combining “tail estimate” technique and some new estimates on solutions. This work improves some recent results about the regularity of random attractors for stochastic reaction-diffusion equations.

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