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

• Autorzy: Xiaoyao Jia , Juanjuan Gao , Xiaoquan Ding
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Gray-Scott equation; Random attractor; Random dynamical system; Multiplicative noise

Kategorie tematyczne

• 35B40: Asymptotic behavior of solutions
• 35K45: Initial value problems for second-order parabolic systems

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2016
• Tom: 14
• Numer: 1
• Strony: 586-602

Daty

wydano

2016-01-01

otrzymano

2016-02-04

zaakceptowano

2016-06-25

online

2016-09-08

Twórcy

autor

Xiaoyao Jia

• School of Mathematics and Statistics, Henan University of Science and Technology, No.263 Kai-Yuan Road, Luo-Long District, Luoyang, Henan Province, 471023,

autor

Juanjuan Gao

• School of Mathematics and Statistics, Henan University of Science and Technology, No.263 Kai-Yuan Road, Luo-Long District, Luoyang, Henan Province, 471023,

autor

Xiaoquan Ding

• School of Mathematics and Statistics, Henan University of Science and Technology, No.263 Kai-Yuan Road, Luo-Long District, Luoyang, Henan Province, 471023,

Identyfikatory

DOI

10.1515/math-2016-0052