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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Format: | Article |
Language: | English |
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Wiley
2014-01-01
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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 |
id | doaj-art-0c02a63b6b2e4c3e83025737829854b9 |
institution | Kabale University |
issn | 1085-3375 1687-0409 |
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 |