Attractor for a Reaction-Diffusion System Modeling Cancer Network

A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are prove...

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Main Authors: Xueyong Chen, Jianwei Shen, Hongxian Zhou
Format: Article
Language:English
Published: Wiley 2014-01-01
Series:Abstract and Applied Analysis
Online Access:http://dx.doi.org/10.1155/2014/420386
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author Xueyong Chen
Jianwei Shen
Hongxian Zhou
author_facet Xueyong Chen
Jianwei Shen
Hongxian Zhou
author_sort Xueyong Chen
collection DOAJ
description A reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω)×L2(Ω) and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.
format Article
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institution Kabale University
issn 1085-3375
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language English
publishDate 2014-01-01
publisher Wiley
record_format Article
series Abstract and Applied Analysis
spelling doaj-art-0c02a63b6b2e4c3e83025737829854b92025-02-03T01:29:04ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/420386420386Attractor for a Reaction-Diffusion System Modeling Cancer NetworkXueyong Chen0Jianwei Shen1Hongxian Zhou2Institute of Applied Mathematics, Xuchang University, Xuchang, Henan 461000, ChinaInstitute of Applied Mathematics, Xuchang University, Xuchang, Henan 461000, ChinaInstitute of Applied Mathematics, Xuchang University, Xuchang, Henan 461000, ChinaA reaction-diffusion cancer network regulated by microRNA is considered in this paper. We study the asymptotic behavior of solution and show the existence of global uniformly bounded solution to the system in a bounded domain Ω⊂Rn. Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in L2(Ω)×L2(Ω) and prove that the solution converges to stable steady states. These results can help to understand the dynamical character of cancer network and propose a new insight to study the mechanism of cancer. In the end, the numerical simulation shows that the analytical results agree with numerical simulation.http://dx.doi.org/10.1155/2014/420386
spellingShingle Xueyong Chen
Jianwei Shen
Hongxian Zhou
Attractor for a Reaction-Diffusion System Modeling Cancer Network
Abstract and Applied Analysis
title Attractor for a Reaction-Diffusion System Modeling Cancer Network
title_full Attractor for a Reaction-Diffusion System Modeling Cancer Network
title_fullStr Attractor for a Reaction-Diffusion System Modeling Cancer Network
title_full_unstemmed Attractor for a Reaction-Diffusion System Modeling Cancer Network
title_short Attractor for a Reaction-Diffusion System Modeling Cancer Network
title_sort attractor for a reaction diffusion system modeling cancer network
url http://dx.doi.org/10.1155/2014/420386
work_keys_str_mv AT xueyongchen attractorforareactiondiffusionsystemmodelingcancernetwork
AT jianweishen attractorforareactiondiffusionsystemmodelingcancernetwork
AT hongxianzhou attractorforareactiondiffusionsystemmodelingcancernetwork