Open Access
2014 Attractor for a Reaction-Diffusion System Modeling Cancer Network
Xueyong Chen, Jianwei Shen, Hongxian Zhou
Abstr. Appl. Anal. 2014(SI37): 1-8 (2014). DOI: 10.1155/2014/420386


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 ΩRn. 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.


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Xueyong Chen. Jianwei Shen. Hongxian Zhou. "Attractor for a Reaction-Diffusion System Modeling Cancer Network." Abstr. Appl. Anal. 2014 (SI37) 1 - 8, 2014.


Published: 2014
First available in Project Euclid: 6 October 2014

zbMATH: 07022360
MathSciNet: MR3198189
Digital Object Identifier: 10.1155/2014/420386

Rights: Copyright © 2014 Hindawi

Vol.2014 • No. SI37 • 2014
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