201. Asymptotic dynamics of an anti-angiogenic system in tumour growth
- Author
-
Qingshan Zhang and Xue Yu
- Subjects
Physics ,0209 industrial biotechnology ,Control and Optimization ,Control engineering systems. Automatic machinery (General) ,Quantitative Biology::Tissues and Organs ,Boundary problem ,Anti angiogenic ,asymptotic behaviour ,02 engineering and technology ,Quantitative Biology::Cell Behavior ,Asymptotic dynamics ,Systems engineering ,TA168 ,020901 industrial engineering & automation ,Artificial Intelligence ,Control and Systems Engineering ,Bounded function ,global solution ,TJ212-225 ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,020201 artificial intelligence & image processing ,antiangiogenesis - 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 $ (\bar {n}_0, 0, 0) $ as $ t\to \infty $ , where $ \bar {n}_0 $ is the spatial mean of the initial data for the endothelial cell tip density.
- Published
- 2021