Asymptotic dynamics of an anti-angiogenic system in tumour growth. (1st April 2021)

• Record Type: Journal Article
• Authors: Yu, Xue; Zhang, Qingshan
• Is Part Of: Systems science & control engineering. Volume 9(2021)Supplement 1
• Page Start: 24
• Page End: 29
• Publication Date: 2021-04-01
• Subjects: Antiangiogenesis -- global solution -- asymptotic behaviour; 35K55 -- 35Q92 -- 35B40; System theory -- Periodicals; Automatic control -- Periodicals; 003.05
• DOI: 10.1080/21642583.2020.1865215
• Languages: English
• ISSNs: 2164-2583

Abstract

Abstract : This paper deals with the Neumann initial boundary problem for anti-angiogenic system in tumour growth. The known results show that the problem possesses a unique global-in-time bounded classical solution for some sufficiently smooth initial data. For the large time behaviour of the global solution, by establishing some estimates based on semigroup theory, we prove that the solution approaches to the homogeneous steady state ( n ¯ 0, 0, 0 ) as t → ∞, where n ¯ 0 is the spatial mean of the initial data for the endothelial cell tip density.