On a chemotaxis model with competitive terms arising in angiogenesis

Manuel Delgado; Inmaculada Gayte; Cristian Morales-Rodrigo; Antonio Suárez

doi:10.3934/dcdss.2020010

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2020, Volume 13, Issue 2: 177-202. Doi: 10.3934/dcdss.2020010

This issue Previous Article Global existence in the 1D quasilinear parabolic-elliptic chemotaxis system with critical nonlinearity Next Article Global asymptotic stability in a chemotaxis-growth model for tumor invasion

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
* Corresponding author: C. Morales-Rodrigo

Received: April 30, 2017

Revised: January 31, 2018

Published: February 2020

Supported by MINECO (Spain) grant MTM2015-69875P.

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Abstract

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.

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Mathematics Subject Classification: Primary: 35K45, 35K57; Secondary: 92C17.

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Figure 1. A particular example of domain $ \Omega $.

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