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Attractor for a Reaction‐Diffusion System Modeling Cancer Network

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Listed:
  • Xueyong Chen
  • Jianwei Shen
  • Hongxian Zhou

Abstract

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.

Suggested Citation

  • Xueyong Chen & Jianwei Shen & Hongxian Zhou, 2014. "Attractor for a Reaction‐Diffusion System Modeling Cancer Network," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:420386
    DOI: 10.1155/2014/420386
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    References listed on IDEAS

    as
    1. Xueyong Chen & Jianwei Shen, 2013. "Global Attractor for a Chemotaxis Model with Reaction Term," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-8, July.
    2. Xueyong Chen & Jianwei Shen, 2013. "Global Attractor for a Chemotaxis Model with Reaction Term," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    3. Victor Ambros, 2004. "The functions of animal microRNAs," Nature, Nature, vol. 431(7006), pages 350-355, September.
    Full references (including those not matched with items on IDEAS)

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