# American Institute of Mathematical Sciences

## On a chemotaxis model with competitive terms arising in angiogenesis

 Dpto. de Ecuaciones Diferenciales y Análisis Numérico, Fac. de Matemáticas, Universidad de Sevilla, Calle Tarfia s/n, 41012, Sevilla, Spain

* Corresponding author: C. Morales-Rodrigo

Received  May 2017 Revised  February 2018 Published  January 2019

Fund Project: Supported by MINECO (Spain) grant MTM2015-69875P

In this paper we study an anti-angiogenic therapy model that deactivates the tumor angiogenic factors. The model consists of four parabolic equations and considers the chemotaxis and a logistic law for the endothelial cells and several boundary conditions, some of them are non homogeneous. We study the parabolic problem, proving the existence of a unique global positive solution for positive initial conditions, and the stationary problem, justifying the existence of one real number, an eigenvalue of a certain problem, which determines if the semi-trivial solutions are stable or unstable and the existence of a coexistence state.

Citation: Manuel Delgado, Inmaculada Gayte, Cristian Morales-Rodrigo, Antonio Suárez. On a chemotaxis model with competitive terms arising in angiogenesis. Discrete & Continuous Dynamical Systems - S, doi: 10.3934/dcdss.2020010
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