Attractor for a reaction-diffusion system modeling cancer network
type: Item
instance of: scholarly article
title: Attractor for a reaction-diffusion system modeling cancer network
zbMATH Open document ID: 1470.35178
DOI: 10.1155/2014/420386
author: Xueyong Chen
author: Jianwei Shen
author: Hongxian Zhou
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: 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 \(\Omega \subset \mathbb R^n\). Some estimates and asymptotic compactness of the solutions are proved. As a result, we establish the existence of the global attractor in \(L^2(\Omega) \times L^2(\Omega)\) 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.
Mathematics Subject Classification ID: 35K51
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q92
Mathematics Subject Classification ID: 92C15
Mathematics Subject Classification ID: 92C17
Mathematics Subject Classification ID: 92D20
zbMATH DE Number: 7022360
Wikidata QID: Q59037858
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/420386
OpenAlex ID: W2110890836
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description: scientific article; zbMATH DE number 7022360