Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise

Xiaoyao Jia, Juanjuan Gao, and Xiaoquan Ding. "Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise." Open Mathematics 14.1 (2016): 586-602. <http://eudml.org/doc/286754>.

@article{XiaoyaoJia2016,
abstract = {In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.},
author = {Xiaoyao Jia, Juanjuan Gao, Xiaoquan Ding},
journal = {Open Mathematics},
keywords = {Gray-Scott equation; Random attractor; Random dynamical system; Multiplicative noise; random attractor; random dynamical system; multiplicative noise},
language = {eng},
number = {1},
pages = {586-602},
title = {Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise},
url = {http://eudml.org/doc/286754},
volume = {14},
year = {2016},
}

TY - JOUR
AU - Xiaoyao Jia
AU - Juanjuan Gao
AU - Xiaoquan Ding
TI - Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise
JO - Open Mathematics
PY - 2016
VL - 14
IS - 1
SP - 586
EP - 602
AB - In this paper, we consider the existence of a pullback attractor for the random dynamical system generated by stochastic two-compartment Gray-Scott equation for a multiplicative noise with the homogeneous Neumann boundary condition on a bounded domain of space dimension n ≤ 3. We first show that the stochastic Gray-Scott equation generates a random dynamical system by transforming this stochastic equation into a random one. We also show that the existence of a random attractor for the stochastic equation follows from the conjugation relation between systems. Then, we prove pullback asymptotical compactness of solutions through the uniform estimate on the solutions. Finally, we obtain the existence of a pullback attractor.
LA - eng
KW - Gray-Scott equation; Random attractor; Random dynamical system; Multiplicative noise; random attractor; random dynamical system; multiplicative noise
UR - http://eudml.org/doc/286754
ER -