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



Hai-Yang Jin (School of Mathematics, South China University of Technology, Guangzhou, China)

Jiao Xu (SUSTech International Center for Mathematics, Southern University of Science and Technology, Shenzhen, China)


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.


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