Contents Online
Communications in Mathematical Sciences
Volume 19 (2021)
Number 4
Analysis of the role of convection in a system describing the tumor-induced angiogenesis
Pages: 1033 – 1049
DOI: https://dx.doi.org/10.4310/CMS.2021.v19.n4.a7
Authors
Abstract
In this paper, we shall study the initial-boundary value problem of a mathematical model describing the branching of capillary sprouts during angiogenesis in one dimensional space. Under homogeneous Neumann boundary conditions, we show the existence of a unique global classical solution with uniform-in-time bound for all suitably regular initial data. Moreover, we show that the unique solution will exponentially converge to a non-trivial constant steady state as time tends to infinity under some appropriate conditions on the parameters.
Keywords
boundedness, chemotaxis, haptotaxis, convergence rate
2010 Mathematics Subject Classification
35A01, 35B40, 35K55, 35Q92, 92C17
Received 14 April 2020
Accepted 26 November 2020
Published 18 June 2021