Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise
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...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2016-01-01
|
| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0052/math-2016-0052.xml?format=INT |
| _version_ | 1818126442735599616 |
|---|---|
| author | Jia Xiaoyao Gao Juanjuan Ding Xiaoquan |
| author_facet | Jia Xiaoyao Gao Juanjuan Ding Xiaoquan |
| author_sort | Jia Xiaoyao |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T07:01:32Z |
| format | Article |
| id | doaj.art-82eddac6e28b47a1bfca70761405841e |
| institution | Directory Open Access Journal |
| issn | 2391-5455 |
| language | English |
| last_indexed | 2024-12-11T07:01:32Z |
| publishDate | 2016-01-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj.art-82eddac6e28b47a1bfca70761405841e2022-12-22T01:16:36ZengDe GruyterOpen Mathematics2391-54552016-01-0114158660210.1515/math-2016-0052math-2016-0052Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noiseJia Xiaoyao0Gao Juanjuan1Ding Xiaoquan2School of Mathematics and Statistics, Henan University of Science and Technology, No.263 Kai-Yuan Road, Luo-Long District, Luoyang, Henan Province, 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, No.263 Kai-Yuan Road, Luo-Long District, Luoyang, Henan Province, 471023, ChinaSchool of Mathematics and Statistics, Henan University of Science and Technology, No.263 Kai-Yuan Road, Luo-Long District, Luoyang, Henan Province, 471023, ChinaIn 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.http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0052/math-2016-0052.xml?format=INTgray-scott equationrandom attractorrandom dynamical systemmultiplicative noise35k4535b40 |
| spellingShingle | Jia Xiaoyao Gao Juanjuan Ding Xiaoquan Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise Open Mathematics gray-scott equation random attractor random dynamical system multiplicative noise 35k45 35b40 |
| title | Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise |
| title_full | Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise |
| title_fullStr | Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise |
| title_full_unstemmed | Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise |
| title_short | Random attractors for stochastic two-compartment Gray-Scott equations with a multiplicative noise |
| title_sort | random attractors for stochastic two compartment gray scott equations with a multiplicative noise |
| topic | gray-scott equation random attractor random dynamical system multiplicative noise 35k45 35b40 |
| url | http://www.degruyter.com/view/j/math.2016.14.issue-1/math-2016-0052/math-2016-0052.xml?format=INT |
| work_keys_str_mv | AT jiaxiaoyao randomattractorsforstochastictwocompartmentgrayscottequationswithamultiplicativenoise AT gaojuanjuan randomattractorsforstochastictwocompartmentgrayscottequationswithamultiplicativenoise AT dingxiaoquan randomattractorsforstochastictwocompartmentgrayscottequationswithamultiplicativenoise |